2t^2-30t=-52

Solution for 2t^2-30t=-52 equation:

2t^2-30t=-52

We move all terms to the left:

2t^2-30t-(-52)=0

We add all the numbers together, and all the variables

2t^2-30t+52=0

a = 2; b = -30; c = +52;
Δ = b2-4ac
Δ = -302-4·2·52
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-22}{2*2}=\frac{8}{4}
=2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+22}{2*2}=\frac{52}{4}
=13
$