9t^2-5t=12

Solution for 9t^2-5t=12 equation:

9t^2-5t=12

We move all terms to the left:

9t^2-5t-(12)=0

a = 9; b = -5; c = -12;
Δ = b2-4ac
Δ = -52-4·9·(-12)
Δ = 457
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{457}}{2*9}=\frac{5-\sqrt{457}}{18}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{457}}{2*9}=\frac{5+\sqrt{457}}{18}
$