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(4x-8)(3x-5)=232
We move all terms to the left:
(4x-8)(3x-5)-(232)=0
We multiply parentheses ..
(+12x^2-20x-24x+40)-232=0
We get rid of parentheses
12x^2-20x-24x+40-232=0
We add all the numbers together, and all the variables
12x^2-44x-192=0
a = 12; b = -44; c = -192;
Δ = b2-4ac
Δ = -442-4·12·(-192)
Δ = 11152
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{11152}=\sqrt{16*697}=\sqrt{16}*\sqrt{697}=4\sqrt{697}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{697}}{2*12}=\frac{44-4\sqrt{697}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{697}}{2*12}=\frac{44+4\sqrt{697}}{24} $
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