(2x+6)(2x+6)=74

Solution for (2x+6)(2x+6)=74 equation:

(2x+6)(2x+6)=74

We move all terms to the left:

(2x+6)(2x+6)-(74)=0

We multiply parentheses ..

(+4x^2+12x+12x+36)-74=0

We get rid of parentheses

4x^2+12x+12x+36-74=0

We add all the numbers together, and all the variables

4x^2+24x-38=0

a = 4; b = 24; c = -38;
Δ = b2-4ac
Δ = 242-4·4·(-38)
Δ = 1184
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:

$\sqrt{\Delta}=\sqrt{1184}=\sqrt{16*74}=\sqrt{16}*\sqrt{74}=4\sqrt{74}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{74}}{2*4}=\frac{-24-4\sqrt{74}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{74}}{2*4}=\frac{-24+4\sqrt{74}}{8}
$