-5t^2+15t=6

Solution for -5t^2+15t=6 equation:

-5t^2+15t=6

We move all terms to the left:

-5t^2+15t-(6)=0

a = -5; b = 15; c = -6;
Δ = b2-4ac
Δ = 152-4·(-5)·(-6)
Δ = 105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{105}}{2*-5}=\frac{-15-\sqrt{105}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{105}}{2*-5}=\frac{-15+\sqrt{105}}{-10}
$