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-6b^2-24b+10=0
a = -6; b = -24; c = +10;
Δ = b2-4ac
Δ = -242-4·(-6)·10
Δ = 816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{51}}{2*-6}=\frac{24-4\sqrt{51}}{-12} $$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{51}}{2*-6}=\frac{24+4\sqrt{51}}{-12} $
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