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11x(3x-8)=44
We move all terms to the left:
11x(3x-8)-(44)=0
We multiply parentheses
33x^2-88x-44=0
a = 33; b = -88; c = -44;
Δ = b2-4ac
Δ = -882-4·33·(-44)
Δ = 13552
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{13552}=\sqrt{1936*7}=\sqrt{1936}*\sqrt{7}=44\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-44\sqrt{7}}{2*33}=\frac{88-44\sqrt{7}}{66} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+44\sqrt{7}}{2*33}=\frac{88+44\sqrt{7}}{66} $
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