x^2+4.5x=35.5

Solution for x^2+4.5x=35.5 equation:

x^2+4.5x=35.5

We move all terms to the left:

x^2+4.5x-(35.5)=0

We add all the numbers together, and all the variables

x^2+4.5x-35.5=0

a = 1; b = 4.5; c = -35.5;
Δ = b2-4ac
Δ = 4.52-4·1·(-35.5)
Δ = 162.25
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{162.25}}{2*1}=\frac{-4.5-\sqrt{162.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4.5)+\sqrt{162.25}}{2*1}=\frac{-4.5+\sqrt{162.25}}{2}
$