x^2=12.1875x-5.4375

Solution for x^2=12.1875x-5.4375 equation:

x^2=12.1875x-5.4375

We move all terms to the left:

x^2-(12.1875x-5.4375)=0

We get rid of parentheses

x^2-12.1875x+5.4375=0

a = 1; b = -12.1875; c = +5.4375;
Δ = b2-4ac
Δ = -12.18752-4·1·5.4375
Δ = 126.78515625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12.1875)-\sqrt{126.78515625}}{2*1}=\frac{12.1875-\sqrt{126.78515625}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12.1875)+\sqrt{126.78515625}}{2*1}=\frac{12.1875+\sqrt{126.78515625}}{2}
$