12x^2-78x+93.5=62.5

Solution for 12x^2-78x+93.5=62.5 equation:

12x^2-78x+93.5=62.5

We move all terms to the left:

12x^2-78x+93.5-(62.5)=0

We add all the numbers together, and all the variables

12x^2-78x+31=0

a = 12; b = -78; c = +31;
Δ = b2-4ac
Δ = -782-4·12·31
Δ = 4596
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:

$\sqrt{\Delta}=\sqrt{4596}=\sqrt{4*1149}=\sqrt{4}*\sqrt{1149}=2\sqrt{1149}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-2\sqrt{1149}}{2*12}=\frac{78-2\sqrt{1149}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+2\sqrt{1149}}{2*12}=\frac{78+2\sqrt{1149}}{24}
$