X^2+45x=506.25

Solution for X^2+45x=506.25 equation:

X^2+45X=506.25

We move all terms to the left:

X^2+45X-(506.25)=0

We add all the numbers together, and all the variables

X^2+45X-506.25=0

a = 1; b = 45; c = -506.25;
Δ = b2-4ac
Δ = 452-4·1·(-506.25)
Δ = 4050
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4050}=\sqrt{2025*2}=\sqrt{2025}*\sqrt{2}=45\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-45\sqrt{2}}{2*1}=\frac{-45-45\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+45\sqrt{2}}{2*1}=\frac{-45+45\sqrt{2}}{2}
$