x^2+.25x=6300

Solution for x^2+.25x=6300 equation:

x^2+.25x=6300

We move all terms to the left:

x^2+.25x-(6300)=0

a = 1; b = .25; c = -6300;
Δ = b2-4ac
Δ = .252-4·1·(-6300)
Δ = 25200.0625
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{-(.25)-\sqrt{25200.0625}}{2*1}=\frac{-0.25-\sqrt{25200.0625}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(.25)+\sqrt{25200.0625}}{2*1}=\frac{-0.25+\sqrt{25200.0625}}{2}
$