x^2-21.75x=-15.15

Solution for x^2-21.75x=-15.15 equation:

x^2-21.75x=-15.15

We move all terms to the left:

x^2-21.75x-(-15.15)=0

We add all the numbers together, and all the variables

x^2-21.75x+15.15=0

a = 1; b = -21.75; c = +15.15;
Δ = b2-4ac
Δ = -21.752-4·1·15.15
Δ = 412.4625
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{-(-21.75)-\sqrt{412.4625}}{2*1}=\frac{21.75-\sqrt{412.4625}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21.75)+\sqrt{412.4625}}{2*1}=\frac{21.75+\sqrt{412.4625}}{2}
$