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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

8x^2+12x-176=0

a = 8; b = 12; c = -176;
Δ = b2-4ac
Δ = 122-4·8·(-176)
Δ = 5776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5776}=76$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-76}{2*8}=\frac{-88}{16}
=-5+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+76}{2*8}=\frac{64}{16}
=4
$