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x(12x-44)=32
We move all terms to the left:
x(12x-44)-(32)=0
We multiply parentheses
12x^2-44x-32=0
a = 12; b = -44; c = -32;
Δ = b2-4ac
Δ = -442-4·12·(-32)
Δ = 3472
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3472}=\sqrt{16*217}=\sqrt{16}*\sqrt{217}=4\sqrt{217}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{217}}{2*12}=\frac{44-4\sqrt{217}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{217}}{2*12}=\frac{44+4\sqrt{217}}{24} $
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