What is the answer to Ax+Bsqrt(x)-C=0 ?

The answer to Ax+Bsqrt(x)-C=0 is x=(2AC+B^2+Bsqrt(4AC+B^2))/(2A^2),x=(2AC+B^2-Bsqrt(4AC+B^2))/(2A^2)

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Ax+Bsqrt(x)-C=0

A x + B x - C = 0

x = \frac{2 A C + B ^{2} + B 4 A C + B ^{2}}{2 A ^{2}}, x = \frac{2 A C + B ^{2} - B 4 A C + B ^{2}}{2 A ^{2}}

Solution steps

A x + B x - C = 0

Remove square roots

B^{2} x = A^{2} x^{2} - 2 A C x + C^{2}

Solve

B^{2} x = A^{2} x^{2} - 2 A C x + C^{2} : x = \frac{2 A C + B ^{2} + B 4 A C + B ^{2}}{2 A ^{2}}, x = \frac{2 A C + B ^{2} - B 4 A C + B ^{2}}{2 A ^{2}}

x = \frac{2 A C + B ^{2} + B 4 A C + B ^{2}}{2 A ^{2}}, x = \frac{2 A C + B ^{2} - B 4 A C + B ^{2}}{2 A ^{2}}

y, y^{\frac{2}{3}} = x

\frac{x}{4} = 2 x - 15

(- 3 x + 18)^{\frac{1}{2}} = x

x = 3 x + 1

4 (x - 1)^{\frac{2}{3}} = 0

What is the answer to Ax+Bsqrt(x)-C=0 ?
The answer to Ax+Bsqrt(x)-C=0 is x=(2AC+B^2+Bsqrt(4AC+B^2))/(2A^2),x=(2AC+B^2-Bsqrt(4AC+B^2))/(2A^2)