0=t^2-14t+30

Solution for 0=t^2-14t+30 equation:

0=t^2-14t+30

We move all terms to the left:

0-(t^2-14t+30)=0

We add all the numbers together, and all the variables

-(t^2-14t+30)=0

We get rid of parentheses

-t^2+14t-30=0

We add all the numbers together, and all the variables

-1t^2+14t-30=0

a = -1; b = 14; c = -30;
Δ = b2-4ac
Δ = 142-4·(-1)·(-30)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{19}}{2*-1}=\frac{-14-2\sqrt{19}}{-2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{19}}{2*-1}=\frac{-14+2\sqrt{19}}{-2}
$