5t^2-40t=225

Solution for 5t^2-40t=225 equation:

5t^2-40t=225

We move all terms to the left:

5t^2-40t-(225)=0

a = 5; b = -40; c = -225;
Δ = b2-4ac
Δ = -402-4·5·(-225)
Δ = 6100
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:

$\sqrt{\Delta}=\sqrt{6100}=\sqrt{100*61}=\sqrt{100}*\sqrt{61}=10\sqrt{61}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-10\sqrt{61}}{2*5}=\frac{40-10\sqrt{61}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+10\sqrt{61}}{2*5}=\frac{40+10\sqrt{61}}{10}
$