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11x^2-84x+24=0
a = 11; b = -84; c = +24;
Δ = b2-4ac
Δ = -842-4·11·24
Δ = 6000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6000}=\sqrt{400*15}=\sqrt{400}*\sqrt{15}=20\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-20\sqrt{15}}{2*11}=\frac{84-20\sqrt{15}}{22} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+20\sqrt{15}}{2*11}=\frac{84+20\sqrt{15}}{22} $
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