5t^2-75t=850

Solution for 5t^2-75t=850 equation:

5t^2-75t=850

We move all terms to the left:

5t^2-75t-(850)=0

a = 5; b = -75; c = -850;
Δ = b2-4ac
Δ = -752-4·5·(-850)
Δ = 22625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{22625}=\sqrt{25*905}=\sqrt{25}*\sqrt{905}=5\sqrt{905}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-5\sqrt{905}}{2*5}=\frac{75-5\sqrt{905}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+5\sqrt{905}}{2*5}=\frac{75+5\sqrt{905}}{10}
$