219736.50=257.5^2+257.5x+x^2

Solution for 219736.50=257.5^2+257.5x+x^2 equation:

219736.50=257.5^2+257.5x+x^2

We move all terms to the left:

219736.50-(257.5^2+257.5x+x^2)=0

We add all the numbers together, and all the variables

-(257.5^2+257.5x+x^2)+219736.5=0

We get rid of parentheses

-x^2-257.5x+219736.5-257.5^2=0

We add all the numbers together, and all the variables

-1x^2-257.5x+153430.25=0

a = -1; b = -257.5; c = +153430.25;
Δ = b2-4ac
Δ = -257.52-4·(-1)·153430.25
Δ = 680027.25
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{-(-257.5)-\sqrt{680027.25}}{2*-1}=\frac{257.5-\sqrt{680027.25}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-257.5)+\sqrt{680027.25}}{2*-1}=\frac{257.5+\sqrt{680027.25}}{-2}
$