5t^2+20t=11760

Solution for 5t^2+20t=11760 equation:

5t^2+20t=11760

We move all terms to the left:

5t^2+20t-(11760)=0

a = 5; b = 20; c = -11760;
Δ = b2-4ac
Δ = 202-4·5·(-11760)
Δ = 235600
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:

$\sqrt{\Delta}=\sqrt{235600}=\sqrt{400*589}=\sqrt{400}*\sqrt{589}=20\sqrt{589}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20\sqrt{589}}{2*5}=\frac{-20-20\sqrt{589}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20\sqrt{589}}{2*5}=\frac{-20+20\sqrt{589}}{10}
$