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6(x-1)(3x-11)=-7
We move all terms to the left:
6(x-1)(3x-11)-(-7)=0
We add all the numbers together, and all the variables
6(x-1)(3x-11)+7=0
We multiply parentheses ..
6(+3x^2-11x-3x+11)+7=0
We multiply parentheses
18x^2-66x-18x+66+7=0
We add all the numbers together, and all the variables
18x^2-84x+73=0
a = 18; b = -84; c = +73;
Δ = b2-4ac
Δ = -842-4·18·73
Δ = 1800
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-30\sqrt{2}}{2*18}=\frac{84-30\sqrt{2}}{36} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+30\sqrt{2}}{2*18}=\frac{84+30\sqrt{2}}{36} $
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