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(6x+44)(-10x+65)=117
We move all terms to the left:
(6x+44)(-10x+65)-(117)=0
We multiply parentheses ..
(-60x^2+390x-440x+2860)-117=0
We get rid of parentheses
-60x^2+390x-440x+2860-117=0
We add all the numbers together, and all the variables
-60x^2-50x+2743=0
a = -60; b = -50; c = +2743;
Δ = b2-4ac
Δ = -502-4·(-60)·2743
Δ = 660820
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{660820}=\sqrt{4*165205}=\sqrt{4}*\sqrt{165205}=2\sqrt{165205}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{165205}}{2*-60}=\frac{50-2\sqrt{165205}}{-120} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{165205}}{2*-60}=\frac{50+2\sqrt{165205}}{-120} $
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