(9x-2)(5x+7)=57

Solution for (9x-2)(5x+7)=57 equation:

(9x-2)(5x+7)=57

We move all terms to the left:

(9x-2)(5x+7)-(57)=0

We multiply parentheses ..

(+45x^2+63x-10x-14)-57=0

We get rid of parentheses

45x^2+63x-10x-14-57=0

We add all the numbers together, and all the variables

45x^2+53x-71=0

a = 45; b = 53; c = -71;
Δ = b2-4ac
Δ = 532-4·45·(-71)
Δ = 15589
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(53)-\sqrt{15589}}{2*45}=\frac{-53-\sqrt{15589}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(53)+\sqrt{15589}}{2*45}=\frac{-53+\sqrt{15589}}{90}
$