3t^2-10t-15=0

Solution for 3t^2-10t-15=0 equation:

3t^2-10t-15=0

a = 3; b = -10; c = -15;
Δ = b2-4ac
Δ = -102-4·3·(-15)
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{70}}{2*3}=\frac{10-2\sqrt{70}}{6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{70}}{2*3}=\frac{10+2\sqrt{70}}{6}
$