t^2-14t=-15

Solution for t^2-14t=-15 equation:

t^2-14t=-15

We move all terms to the left:

t^2-14t-(-15)=0

We add all the numbers together, and all the variables

t^2-14t+15=0

a = 1; b = -14; c = +15;
Δ = b2-4ac
Δ = -142-4·1·15
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{34}}{2*1}=\frac{14-2\sqrt{34}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{34}}{2*1}=\frac{14+2\sqrt{34}}{2}
$