x^2-8x+12=0.25x+2

Solution for x^2-8x+12=0.25x+2 equation:

x^2-8x+12=0.25x+2

We move all terms to the left:

x^2-8x+12-(0.25x+2)=0

We get rid of parentheses

x^2-8x-0.25x-2+12=0

We add all the numbers together, and all the variables

x^2-8.25x+10=0

a = 1; b = -8.25; c = +10;
Δ = b2-4ac
Δ = -8.252-4·1·10
Δ = 28.0625
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{-(-8.25)-\sqrt{28.0625}}{2*1}=\frac{8.25-\sqrt{28.0625}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8.25)+\sqrt{28.0625}}{2*1}=\frac{8.25+\sqrt{28.0625}}{2}
$