5t^2-35t=15

Solution for 5t^2-35t=15 equation:

5t^2-35t=15

We move all terms to the left:

5t^2-35t-(15)=0

a = 5; b = -35; c = -15;
Δ = b2-4ac
Δ = -352-4·5·(-15)
Δ = 1525
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:

$\sqrt{\Delta}=\sqrt{1525}=\sqrt{25*61}=\sqrt{25}*\sqrt{61}=5\sqrt{61}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-5\sqrt{61}}{2*5}=\frac{35-5\sqrt{61}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+5\sqrt{61}}{2*5}=\frac{35+5\sqrt{61}}{10}
$