x^2-43.5x=-14.5

Solution for x^2-43.5x=-14.5 equation:

x^2-43.5x=-14.5

We move all terms to the left:

x^2-43.5x-(-14.5)=0

We add all the numbers together, and all the variables

x^2-43.5x+14.5=0

a = 1; b = -43.5; c = +14.5;
Δ = b2-4ac
Δ = -43.52-4·1·14.5
Δ = 1834.25
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{-(-43.5)-\sqrt{1834.25}}{2*1}=\frac{43.5-\sqrt{1834.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43.5)+\sqrt{1834.25}}{2*1}=\frac{43.5+\sqrt{1834.25}}{2}
$