100x-5x^2=315

Solution for 100x-5x^2=315 equation:

100x-5x^2=315

We move all terms to the left:

100x-5x^2-(315)=0

a = -5; b = 100; c = -315;
Δ = b2-4ac
Δ = 1002-4·(-5)·(-315)
Δ = 3700
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:

$\sqrt{\Delta}=\sqrt{3700}=\sqrt{100*37}=\sqrt{100}*\sqrt{37}=10\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-10\sqrt{37}}{2*-5}=\frac{-100-10\sqrt{37}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+10\sqrt{37}}{2*-5}=\frac{-100+10\sqrt{37}}{-10}
$