(x+4)(2x-7)=90

Solution for (x+4)(2x-7)=90 equation:

(x+4)(2x-7)=90

We move all terms to the left:

(x+4)(2x-7)-(90)=0

We multiply parentheses ..

(+2x^2-7x+8x-28)-90=0

We get rid of parentheses

2x^2-7x+8x-28-90=0

We add all the numbers together, and all the variables

2x^2+x-118=0

a = 2; b = 1; c = -118;
Δ = b2-4ac
Δ = 12-4·2·(-118)
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{-(1)-3\sqrt{105}}{2*2}=\frac{-1-3\sqrt{105}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{105}}{2*2}=\frac{-1+3\sqrt{105}}{4}
$