(2x-46)(x+2)=90

Solution for (2x-46)(x+2)=90 equation:

(2x-46)(x+2)=90

We move all terms to the left:

(2x-46)(x+2)-(90)=0

We multiply parentheses ..

(+2x^2+4x-46x-92)-90=0

We get rid of parentheses

2x^2+4x-46x-92-90=0

We add all the numbers together, and all the variables

2x^2-42x-182=0

a = 2; b = -42; c = -182;
Δ = b2-4ac
Δ = -422-4·2·(-182)
Δ = 3220
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:

$\sqrt{\Delta}=\sqrt{3220}=\sqrt{4*805}=\sqrt{4}*\sqrt{805}=2\sqrt{805}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{805}}{2*2}=\frac{42-2\sqrt{805}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{805}}{2*2}=\frac{42+2\sqrt{805}}{4}
$