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-12x^2+24x+174=0
a = -12; b = 24; c = +174;
Δ = b2-4ac
Δ = 242-4·(-12)·174
Δ = 8928
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8928}=\sqrt{144*62}=\sqrt{144}*\sqrt{62}=12\sqrt{62}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-12\sqrt{62}}{2*-12}=\frac{-24-12\sqrt{62}}{-24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+12\sqrt{62}}{2*-12}=\frac{-24+12\sqrt{62}}{-24} $
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