C=-5t^2+750

Solution for C=-5t^2+750 equation:

=-5C^2+750

We move all terms to the left:

-(-5C^2+750)=0

We get rid of parentheses

5C^2-750=0

a = 5; b = 0; c = -750;
Δ = b2-4ac
Δ = 02-4·5·(-750)
Δ = 15000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{15000}=\sqrt{2500*6}=\sqrt{2500}*\sqrt{6}=50\sqrt{6}$
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-50\sqrt{6}}{2*5}=\frac{0-50\sqrt{6}}{10}
=-\frac{50\sqrt{6}}{10}
=-5\sqrt{6}
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+50\sqrt{6}}{2*5}=\frac{0+50\sqrt{6}}{10}
=\frac{50\sqrt{6}}{10}
=5\sqrt{6}
$