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(4x+36)(6x-2)=180
We move all terms to the left:
(4x+36)(6x-2)-(180)=0
We multiply parentheses ..
(+24x^2-8x+216x-72)-180=0
We get rid of parentheses
24x^2-8x+216x-72-180=0
We add all the numbers together, and all the variables
24x^2+208x-252=0
a = 24; b = 208; c = -252;
Δ = b2-4ac
Δ = 2082-4·24·(-252)
Δ = 67456
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{67456}=\sqrt{64*1054}=\sqrt{64}*\sqrt{1054}=8\sqrt{1054}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(208)-8\sqrt{1054}}{2*24}=\frac{-208-8\sqrt{1054}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(208)+8\sqrt{1054}}{2*24}=\frac{-208+8\sqrt{1054}}{48} $
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