360=(2x+4)(2x+6)+140

Solution for 360=(2x+4)(2x+6)+140 equation:

360=(2x+4)(2x+6)+140

We move all terms to the left:

360-((2x+4)(2x+6)+140)=0

We multiply parentheses ..

-((+4x^2+12x+8x+24)+140)+360=0


We calculate terms in parentheses: -((+4x^2+12x+8x+24)+140), so:

(+4x^2+12x+8x+24)+140

We get rid of parentheses

4x^2+12x+8x+24+140

We add all the numbers together, and all the variables

4x^2+20x+164

Back to the equation:

-(4x^2+20x+164)


We get rid of parentheses

-4x^2-20x-164+360=0

We add all the numbers together, and all the variables

-4x^2-20x+196=0

a = -4; b = -20; c = +196;
Δ = b2-4ac
Δ = -202-4·(-4)·196
Δ = 3536
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:

$\sqrt{\Delta}=\sqrt{3536}=\sqrt{16*221}=\sqrt{16}*\sqrt{221}=4\sqrt{221}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{221}}{2*-4}=\frac{20-4\sqrt{221}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{221}}{2*-4}=\frac{20+4\sqrt{221}}{-8}
$