X^2+4.5x=11.5

Solution for X^2+4.5x=11.5 equation:

X^2+4.5X=11.5

We move all terms to the left:

X^2+4.5X-(11.5)=0

We add all the numbers together, and all the variables

X^2+4.5X-11.5=0

a = 1; b = 4.5; c = -11.5;
Δ = b2-4ac
Δ = 4.52-4·1·(-11.5)
Δ = 66.25
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{-(4.5)-\sqrt{66.25}}{2*1}=\frac{-4.5-\sqrt{66.25}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4.5)+\sqrt{66.25}}{2*1}=\frac{-4.5+\sqrt{66.25}}{2}
$