(4x+10)(x-2)=180

Solution for (4x+10)(x-2)=180 equation:

(4x+10)(x-2)=180

We move all terms to the left:

(4x+10)(x-2)-(180)=0

We multiply parentheses ..

(+4x^2-8x+10x-20)-180=0

We get rid of parentheses

4x^2-8x+10x-20-180=0

We add all the numbers together, and all the variables

4x^2+2x-200=0

a = 4; b = 2; c = -200;
Δ = b2-4ac
Δ = 22-4·4·(-200)
Δ = 3204
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:

$\sqrt{\Delta}=\sqrt{3204}=\sqrt{36*89}=\sqrt{36}*\sqrt{89}=6\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6\sqrt{89}}{2*4}=\frac{-2-6\sqrt{89}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6\sqrt{89}}{2*4}=\frac{-2+6\sqrt{89}}{8}
$