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

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

(X+5)(2X-5)=90

We move all terms to the left:

(X+5)(2X-5)-(90)=0

We multiply parentheses ..

(+2X^2-5X+10X-25)-90=0

We get rid of parentheses

2X^2-5X+10X-25-90=0

We add all the numbers together, and all the variables

2X^2+5X-115=0

a = 2; b = 5; c = -115;
Δ = b2-4ac
Δ = 52-4·2·(-115)
Δ = 945
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:

$\sqrt{\Delta}=\sqrt{945}=\sqrt{9*105}=\sqrt{9}*\sqrt{105}=3\sqrt{105}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3\sqrt{105}}{2*2}=\frac{-5-3\sqrt{105}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3\sqrt{105}}{2*2}=\frac{-5+3\sqrt{105}}{4}
$