(5x+2)(25x-8)=9

Solution for (5x+2)(25x-8)=9 equation:

(5x+2)(25x-8)=9

We move all terms to the left:

(5x+2)(25x-8)-(9)=0

We multiply parentheses ..

(+125x^2-40x+50x-16)-9=0

We get rid of parentheses

125x^2-40x+50x-16-9=0

We add all the numbers together, and all the variables

125x^2+10x-25=0

a = 125; b = 10; c = -25;
Δ = b2-4ac
Δ = 102-4·125·(-25)
Δ = 12600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12600}=\sqrt{900*14}=\sqrt{900}*\sqrt{14}=30\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-30\sqrt{14}}{2*125}=\frac{-10-30\sqrt{14}}{250}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+30\sqrt{14}}{2*125}=\frac{-10+30\sqrt{14}}{250}
$