-3t^2-15t+17=-6t^2

Solution for -3t^2-15t+17=-6t^2 equation:

-3t^2-15t+17=-6t^2

We move all terms to the left:

-3t^2-15t+17-(-6t^2)=0

We get rid of parentheses

-3t^2+6t^2-15t+17=0

We add all the numbers together, and all the variables

3t^2-15t+17=0

a = 3; b = -15; c = +17;
Δ = b2-4ac
Δ = -152-4·3·17
Δ = 21
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{21}}{2*3}=\frac{15-\sqrt{21}}{6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{21}}{2*3}=\frac{15+\sqrt{21}}{6}
$