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(3x-11)(4x-7)44=180
We move all terms to the left:
(3x-11)(4x-7)44-(180)=0
We multiply parentheses ..
(+12x^2-21x-44x+77)44-180=0
We multiply parentheses
528x^2-924x-1936x+3388-180=0
We add all the numbers together, and all the variables
528x^2-2860x+3208=0
a = 528; b = -2860; c = +3208;
Δ = b2-4ac
Δ = -28602-4·528·3208
Δ = 1404304
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1404304}=\sqrt{16*87769}=\sqrt{16}*\sqrt{87769}=4\sqrt{87769}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2860)-4\sqrt{87769}}{2*528}=\frac{2860-4\sqrt{87769}}{1056} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2860)+4\sqrt{87769}}{2*528}=\frac{2860+4\sqrt{87769}}{1056} $
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