5t^2-35t=20

Solution for 5t^2-35t=20 equation:

5t^2-35t=20

We move all terms to the left:

5t^2-35t-(20)=0

a = 5; b = -35; c = -20;
Δ = b2-4ac
Δ = -352-4·5·(-20)
Δ = 1625
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:

$\sqrt{\Delta}=\sqrt{1625}=\sqrt{25*65}=\sqrt{25}*\sqrt{65}=5\sqrt{65}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-5\sqrt{65}}{2*5}=\frac{35-5\sqrt{65}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+5\sqrt{65}}{2*5}=\frac{35+5\sqrt{65}}{10}
$