12t^2+52t-9=0

Solution for 12t^2+52t-9=0 equation:

12t^2+52t-9=0

a = 12; b = 52; c = -9;
Δ = b2-4ac
Δ = 522-4·12·(-9)
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-56}{2*12}=\frac{-108}{24}
=-4+1/2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+56}{2*12}=\frac{4}{24}
=1/6
$