X=-11.25+.25x^2

Solution for X=-11.25+.25x^2 equation:

X=-11.25+.25X^2

We move all terms to the left:

X-(-11.25+.25X^2)=0

We get rid of parentheses

-.25X^2+X+11.25=0

We add all the numbers together, and all the variables

-0.25X^2+X+11.25=0

a = -0.25; b = 1; c = +11.25;
Δ = b2-4ac
Δ = 12-4·(-0.25)·11.25
Δ = 12.25
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{-(1)-\sqrt{12.25}}{2*-0.25}=\frac{-1-\sqrt{12.25}}{-0.5}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{12.25}}{2*-0.25}=\frac{-1+\sqrt{12.25}}{-0.5}
$