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6x^2-108x+112=0
a = 6; b = -108; c = +112;
Δ = b2-4ac
Δ = -1082-4·6·112
Δ = 8976
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8976}=\sqrt{16*561}=\sqrt{16}*\sqrt{561}=4\sqrt{561}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-4\sqrt{561}}{2*6}=\frac{108-4\sqrt{561}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+4\sqrt{561}}{2*6}=\frac{108+4\sqrt{561}}{12} $
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