6.25x+x^2=56.25

Solution for 6.25x+x^2=56.25 equation:

6.25x+x^2=56.25

We move all terms to the left:

6.25x+x^2-(56.25)=0

We add all the numbers together, and all the variables

x^2+6.25x-56.25=0

a = 1; b = 6.25; c = -56.25;
Δ = b2-4ac
Δ = 6.252-4·1·(-56.25)
Δ = 264.0625
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{-(6.25)-\sqrt{264.0625}}{2*1}=\frac{-6.25-\sqrt{264.0625}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6.25)+\sqrt{264.0625}}{2*1}=\frac{-6.25+\sqrt{264.0625}}{2}
$