2/5 x^2+8x-9/4 = 5/7 x+15

Solution

\frac{2}{5} x^{2} + 8 x - \frac{9}{4} = \frac{5}{7} x + 15

x = \frac{- 255 + 98835}{28}, x = - \frac{255 + 98835}{28}

Decimal Notation

x = 2.12072 \dots, x = - 20.33501 \dots

Solution steps

\frac{2}{5} x^{2} + 8 x - \frac{9}{4} = \frac{5}{7} x + 15

Find Least Common Multiplier of

5, 4, 7 : 140

Multiply by LCM=

140

\frac{2}{5} x^{2} \cdot 140 + 8 x \cdot 140 - \frac{9}{4} \cdot 140 = \frac{5}{7} x \cdot 140 + 15 \cdot 140

Simplify

56 x^{2} + 1120 x - 315 = 100 x + 2100

Move

2100

to the left side

56 x^{2} + 1120 x - 2415 = 100 x

Move

100 x

to the left side

56 x^{2} + 1020 x - 2415 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 1020 \pm 102 0 ^{2} - 4 \cdot 56 ( - 2415 )}{2 \cdot 56}

102 0^{2} - 4 \cdot 56 (- 2415) = 498835

x_{1, 2} = \frac{- 1020 \pm 4 98835}{2 \cdot 56}

Separate the solutions

x_{1} = \frac{- 1020 + 4 98835}{2 \cdot 56}, x_{2} = \frac{- 1020 - 4 98835}{2 \cdot 56}

x = \frac{- 1020 + 4 98835}{2 \cdot 56} : \frac{- 255 + 98835}{28}

x = \frac{- 1020 - 4 98835}{2 \cdot 56} : - \frac{255 + 98835}{28}

The solutions to the quadratic equation are:

x = \frac{- 255 + 98835}{28}, x = - \frac{255 + 98835}{28}

x (x - 2) = 5

4 x - x^{2} = 4 - 2 x

0 = \frac{1}{2} x^{2} - 6 x + 21

\frac{7}{5} x + \frac{7}{5} = x^{2} - \frac{8}{5} x - \frac{13}{5}

((x - 1) x - 7 x m^{- 1} + 15) = 0