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(6x+2)(x-4)=180
We move all terms to the left:
(6x+2)(x-4)-(180)=0
We multiply parentheses ..
(+6x^2-24x+2x-8)-180=0
We get rid of parentheses
6x^2-24x+2x-8-180=0
We add all the numbers together, and all the variables
6x^2-22x-188=0
a = 6; b = -22; c = -188;
Δ = b2-4ac
Δ = -222-4·6·(-188)
Δ = 4996
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4996}=\sqrt{4*1249}=\sqrt{4}*\sqrt{1249}=2\sqrt{1249}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{1249}}{2*6}=\frac{22-2\sqrt{1249}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{1249}}{2*6}=\frac{22+2\sqrt{1249}}{12} $
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