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12x^2+44x=15
We move all terms to the left:
12x^2+44x-(15)=0
a = 12; b = 44; c = -15;
Δ = b2-4ac
Δ = 442-4·12·(-15)
Δ = 2656
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2656}=\sqrt{16*166}=\sqrt{16}*\sqrt{166}=4\sqrt{166}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{166}}{2*12}=\frac{-44-4\sqrt{166}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{166}}{2*12}=\frac{-44+4\sqrt{166}}{24} $
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