(15t+6)(2t-5)=0

Solution for (15t+6)(2t-5)=0 equation:

(15t+6)(2t-5)=0

We multiply parentheses ..

(+30t^2-75t+12t-30)=0

We get rid of parentheses

30t^2-75t+12t-30=0

We add all the numbers together, and all the variables

30t^2-63t-30=0

a = 30; b = -63; c = -30;
Δ = b2-4ac
Δ = -632-4·30·(-30)
Δ = 7569
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7569}=87$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-87}{2*30}=\frac{-24}{60}
=-2/5
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+87}{2*30}=\frac{150}{60}
=2+1/2
$