(x+3)(4x-8)=180

Solution for (x+3)(4x-8)=180 equation:

(x+3)(4x-8)=180

We move all terms to the left:

(x+3)(4x-8)-(180)=0

We multiply parentheses ..

(+4x^2-8x+12x-24)-180=0

We get rid of parentheses

4x^2-8x+12x-24-180=0

We add all the numbers together, and all the variables

4x^2+4x-204=0

a = 4; b = 4; c = -204;
Δ = b2-4ac
Δ = 42-4·4·(-204)
Δ = 3280
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:

$\sqrt{\Delta}=\sqrt{3280}=\sqrt{16*205}=\sqrt{16}*\sqrt{205}=4\sqrt{205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{205}}{2*4}=\frac{-4-4\sqrt{205}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{205}}{2*4}=\frac{-4+4\sqrt{205}}{8}
$