What are the solutions to the equation 16x^2=(A+B)x^2+x(10A-10B-C)+25A-75B-15C ?

The solutions to the equation 16x^2=(A+B)x^2+x(10A-10B-C)+25A-75B-15C are

Find the zeros of 16x^2=(A+B)x^2+x(10A-10B-C)+25A-75B-15C

The zeros of 16x^2=(A+B)x^2+x(10A-10B-C)+25A-75B-15C are

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16 x^{2} = (A + B) x^{2} + x (10 A - 10 B - C) + 25 A - 75 B - 15 C

x = \frac{- 10 A + 10 B + C + 40 A C + 1600 A + 400 B ^{2} - 4800 B + C ^{2} + 80 BC - 960 C}{2 ( A + B - 16 )}, x = \frac{- 10 A + 10 B + C - 40 A C + 1600 A + 400 B ^{2} - 4800 B + C ^{2} + 80 BC - 960 C}{2 ( A + B - 16 )}; A + B - 16 \neq = 0

Solution steps

16 x^{2} = (A + B) x^{2} + x (10 A - 10 B - C) + 25 A - 75 B - 15 C

Switch sides

(A + B) x^{2} + x (10 A - 10 B - C) + 25 A - 75 B - 15 C = 16 x^{2}

Move

16 x^{2}

to the left side

(A + B) x^{2} + x (10 A - 10 B - C) + 25 A - 75 B - 15 C - 16 x^{2} = 0

Write in the standard form

a x^{2} + b x + c = 0

(A + B - 16) x^{2} + (10 A - 10 B - C) x + 25 A - 75 B - 15 C = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( 10 A - 10 B - C ) \pm ( 10 A - 10 B - C ) ^{2} - 4 ( A + B - 16 ) ( 25 A - 75 B - 15 C )}{2 ( A + B - 16 )}

Simplify

(10 A - 10 B - C)^{2} - 4 (A + B - 16) (25 A - 75 B - 15 C) : 40 A C + 1600 A + 400 B^{2} - 4800 B + C^{2} + 80 BC - 960 C

x_{1, 2} = \frac{- ( 10 A - 10 B - C ) \pm 40 A C + 1600 A + 400 B ^{2} - 4800 B + C ^{2} + 80 BC - 960 C}{2 ( A + B - 16 )}; A + B - 16 \neq = 0

Separate the solutions

x_{1} = \frac{- ( 10 A - 10 B - C ) + 40 A C + 1600 A + 400 B ^{2} - 4800 B + C ^{2} + 80 BC - 960 C}{2 ( A + B - 16 )}, x_{2} = \frac{- ( 10 A - 10 B - C ) - 40 A C + 1600 A + 400 B ^{2} - 4800 B + C ^{2} + 80 BC - 960 C}{2 ( A + B - 16 )}

x = \frac{- ( 10 A - 10 B - C ) + 40 A C + 1600 A + 400 B ^{2} - 4800 B + C ^{2} + 80 BC - 960 C}{2 ( A + B - 16 )} : \frac{- 10 A + 10 B + C + 40 A C + 1600 A + 400 B ^{2} - 4800 B + C ^{2} + 80 BC - 960 C}{2 ( A + B - 16 )}

x = \frac{- ( 10 A - 10 B - C ) - 40 A C + 1600 A + 400 B ^{2} - 4800 B + C ^{2} + 80 BC - 960 C}{2 ( A + B - 16 )} : \frac{- 10 A + 10 B + C - 40 A C + 1600 A + 400 B ^{2} - 4800 B + C ^{2} + 80 BC - 960 C}{2 ( A + B - 16 )}

The solutions to the quadratic equation are:

x = \frac{- 10 A + 10 B + C + 40 A C + 1600 A + 400 B ^{2} - 4800 B + C ^{2} + 80 BC - 960 C}{2 ( A + B - 16 )}, x = \frac{- 10 A + 10 B + C - 40 A C + 1600 A + 400 B ^{2} - 4800 B + C ^{2} + 80 BC - 960 C}{2 ( A + B - 16 )}; A + B - 16 \neq = 0

7 x^{2} + 14 x + 3 = 0

x^{2} - 25 x = - 100

x^{2} = 45 - 4 x

(x - 3) (x + 7) = 11

2 x^{2} + 3 x - 20 = 0

What are the solutions to the equation 16x^2=(A+B)x^2+x(10A-10B-C)+25A-75B-15C ?
The solutions to the equation 16x^2=(A+B)x^2+x(10A-10B-C)+25A-75B-15C are
Find the zeros of 16x^2=(A+B)x^2+x(10A-10B-C)+25A-75B-15C
The zeros of 16x^2=(A+B)x^2+x(10A-10B-C)+25A-75B-15C are