5t^2-32t=-12

Solution for 5t^2-32t=-12 equation:

5t^2-32t=-12

We move all terms to the left:

5t^2-32t-(-12)=0

We add all the numbers together, and all the variables

5t^2-32t+12=0

a = 5; b = -32; c = +12;
Δ = b2-4ac
Δ = -322-4·5·12
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-28}{2*5}=\frac{4}{10}
=2/5
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+28}{2*5}=\frac{60}{10}
=6
$