15t^2+5t=84

Solution for 15t^2+5t=84 equation:

15t^2+5t=84

We move all terms to the left:

15t^2+5t-(84)=0

a = 15; b = 5; c = -84;
Δ = b2-4ac
Δ = 52-4·15·(-84)
Δ = 5065
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{5065}}{2*15}=\frac{-5-\sqrt{5065}}{30}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{5065}}{2*15}=\frac{-5+\sqrt{5065}}{30}
$