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(4x+6)(11x-6)=180
We move all terms to the left:
(4x+6)(11x-6)-(180)=0
We multiply parentheses ..
(+44x^2-24x+66x-36)-180=0
We get rid of parentheses
44x^2-24x+66x-36-180=0
We add all the numbers together, and all the variables
44x^2+42x-216=0
a = 44; b = 42; c = -216;
Δ = b2-4ac
Δ = 422-4·44·(-216)
Δ = 39780
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{39780}=\sqrt{36*1105}=\sqrt{36}*\sqrt{1105}=6\sqrt{1105}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-6\sqrt{1105}}{2*44}=\frac{-42-6\sqrt{1105}}{88} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+6\sqrt{1105}}{2*44}=\frac{-42+6\sqrt{1105}}{88} $
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