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6x^2=20x+96
We move all terms to the left:
6x^2-(20x+96)=0
We get rid of parentheses
6x^2-20x-96=0
a = 6; b = -20; c = -96;
Δ = b2-4ac
Δ = -202-4·6·(-96)
Δ = 2704
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{2704}=52$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-52}{2*6}=\frac{-32}{12} =-2+2/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+52}{2*6}=\frac{72}{12} =6 $
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