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0=12x^2-78x+93.5
We move all terms to the left:
0-(12x^2-78x+93.5)=0
We add all the numbers together, and all the variables
-(12x^2-78x+93.5)=0
We get rid of parentheses
-12x^2+78x-93.5=0
a = -12; b = 78; c = -93.5;
Δ = b2-4ac
Δ = 782-4·(-12)·(-93.5)
Δ = 1596
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1596}=\sqrt{4*399}=\sqrt{4}*\sqrt{399}=2\sqrt{399}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-2\sqrt{399}}{2*-12}=\frac{-78-2\sqrt{399}}{-24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+2\sqrt{399}}{2*-12}=\frac{-78+2\sqrt{399}}{-24} $
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