(2x+46)(2x-3)=180

Solution for (2x+46)(2x-3)=180 equation:

(2x+46)(2x-3)=180

We move all terms to the left:

(2x+46)(2x-3)-(180)=0

We multiply parentheses ..

(+4x^2-6x+92x-138)-180=0

We get rid of parentheses

4x^2-6x+92x-138-180=0

We add all the numbers together, and all the variables

4x^2+86x-318=0

a = 4; b = 86; c = -318;
Δ = b2-4ac
Δ = 862-4·4·(-318)
Δ = 12484
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:

$\sqrt{\Delta}=\sqrt{12484}=\sqrt{4*3121}=\sqrt{4}*\sqrt{3121}=2\sqrt{3121}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(86)-2\sqrt{3121}}{2*4}=\frac{-86-2\sqrt{3121}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(86)+2\sqrt{3121}}{2*4}=\frac{-86+2\sqrt{3121}}{8}
$