(5x+2)(8x+-25)=90

Solution for (5x+2)(8x+-25)=90 equation:

(5x+2)(8x+-25)=90

We move all terms to the left:

(5x+2)(8x+-25)-(90)=0

We add all the numbers together, and all the variables

(5x+2)(8x-25)-90=0

We multiply parentheses ..

(+40x^2-125x+16x-50)-90=0

We get rid of parentheses

40x^2-125x+16x-50-90=0

We add all the numbers together, and all the variables

40x^2-109x-140=0

a = 40; b = -109; c = -140;
Δ = b2-4ac
Δ = -1092-4·40·(-140)
Δ = 34281
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:

$\sqrt{\Delta}=\sqrt{34281}=\sqrt{9*3809}=\sqrt{9}*\sqrt{3809}=3\sqrt{3809}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-109)-3\sqrt{3809}}{2*40}=\frac{109-3\sqrt{3809}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-109)+3\sqrt{3809}}{2*40}=\frac{109+3\sqrt{3809}}{80}
$