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(3x-3)(4x-14)=180
We move all terms to the left:
(3x-3)(4x-14)-(180)=0
We multiply parentheses ..
(+12x^2-42x-12x+42)-180=0
We get rid of parentheses
12x^2-42x-12x+42-180=0
We add all the numbers together, and all the variables
12x^2-54x-138=0
a = 12; b = -54; c = -138;
Δ = b2-4ac
Δ = -542-4·12·(-138)
Δ = 9540
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9540}=\sqrt{36*265}=\sqrt{36}*\sqrt{265}=6\sqrt{265}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{265}}{2*12}=\frac{54-6\sqrt{265}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{265}}{2*12}=\frac{54+6\sqrt{265}}{24} $
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