(2x-5)(5x+4)=90

Solution for (2x-5)(5x+4)=90 equation:

(2x-5)(5x+4)=90

We move all terms to the left:

(2x-5)(5x+4)-(90)=0

We multiply parentheses ..

(+10x^2+8x-25x-20)-90=0

We get rid of parentheses

10x^2+8x-25x-20-90=0

We add all the numbers together, and all the variables

10x^2-17x-110=0

a = 10; b = -17; c = -110;
Δ = b2-4ac
Δ = -172-4·10·(-110)
Δ = 4689
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:

$\sqrt{\Delta}=\sqrt{4689}=\sqrt{9*521}=\sqrt{9}*\sqrt{521}=3\sqrt{521}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-3\sqrt{521}}{2*10}=\frac{17-3\sqrt{521}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+3\sqrt{521}}{2*10}=\frac{17+3\sqrt{521}}{20}
$