0=7t^2-6t-15

Solution for 0=7t^2-6t-15 equation:

0=7t^2-6t-15

We move all terms to the left:

0-(7t^2-6t-15)=0

We add all the numbers together, and all the variables

-(7t^2-6t-15)=0

We get rid of parentheses

-7t^2+6t+15=0

a = -7; b = 6; c = +15;
Δ = b2-4ac
Δ = 62-4·(-7)·15
Δ = 456
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:

$\sqrt{\Delta}=\sqrt{456}=\sqrt{4*114}=\sqrt{4}*\sqrt{114}=2\sqrt{114}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{114}}{2*-7}=\frac{-6-2\sqrt{114}}{-14}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{114}}{2*-7}=\frac{-6+2\sqrt{114}}{-14}
$