(2x+6)(2x+6)=15

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Solution for (2x+6)(2x+6)=15 equation:



(2x+6)(2x+6)=15
We move all terms to the left:
(2x+6)(2x+6)-(15)=0
We multiply parentheses ..
(+4x^2+12x+12x+36)-15=0
We get rid of parentheses
4x^2+12x+12x+36-15=0
We add all the numbers together, and all the variables
4x^2+24x+21=0
a = 4; b = 24; c = +21;
Δ = b2-4ac
Δ = 242-4·4·21
Δ = 240
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:
$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{15}}{2*4}=\frac{-24-4\sqrt{15}}{8} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{15}}{2*4}=\frac{-24+4\sqrt{15}}{8} $

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