X^2-25n=175

Solution for X^2-25n=175 equation:

X^2-25X=175

We move all terms to the left:

X^2-25X-(175)=0

a = 1; b = -25; c = -175;
Δ = b2-4ac
Δ = -252-4·1·(-175)
Δ = 1325
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:

$\sqrt{\Delta}=\sqrt{1325}=\sqrt{25*53}=\sqrt{25}*\sqrt{53}=5\sqrt{53}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-5\sqrt{53}}{2*1}=\frac{25-5\sqrt{53}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+5\sqrt{53}}{2*1}=\frac{25+5\sqrt{53}}{2}
$