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(4x-4)(6x-22)=180
We move all terms to the left:
(4x-4)(6x-22)-(180)=0
We multiply parentheses ..
(+24x^2-88x-24x+88)-180=0
We get rid of parentheses
24x^2-88x-24x+88-180=0
We add all the numbers together, and all the variables
24x^2-112x-92=0
a = 24; b = -112; c = -92;
Δ = b2-4ac
Δ = -1122-4·24·(-92)
Δ = 21376
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{21376}=\sqrt{64*334}=\sqrt{64}*\sqrt{334}=8\sqrt{334}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-8\sqrt{334}}{2*24}=\frac{112-8\sqrt{334}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+8\sqrt{334}}{2*24}=\frac{112+8\sqrt{334}}{48} $
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