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(3x+6)(2x+8)+24=180
We move all terms to the left:
(3x+6)(2x+8)+24-(180)=0
We add all the numbers together, and all the variables
(3x+6)(2x+8)-156=0
We multiply parentheses ..
(+6x^2+24x+12x+48)-156=0
We get rid of parentheses
6x^2+24x+12x+48-156=0
We add all the numbers together, and all the variables
6x^2+36x-108=0
a = 6; b = 36; c = -108;
Δ = b2-4ac
Δ = 362-4·6·(-108)
Δ = 3888
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3888}=\sqrt{1296*3}=\sqrt{1296}*\sqrt{3}=36\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36\sqrt{3}}{2*6}=\frac{-36-36\sqrt{3}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36\sqrt{3}}{2*6}=\frac{-36+36\sqrt{3}}{12} $
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