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-12x^2+2x+112=0
a = -12; b = 2; c = +112;
Δ = b2-4ac
Δ = 22-4·(-12)·112
Δ = 5380
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5380}=\sqrt{4*1345}=\sqrt{4}*\sqrt{1345}=2\sqrt{1345}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{1345}}{2*-12}=\frac{-2-2\sqrt{1345}}{-24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{1345}}{2*-12}=\frac{-2+2\sqrt{1345}}{-24} $
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