(10t+7)(3t-2)=0

Solution for (10t+7)(3t-2)=0 equation:

(10t+7)(3t-2)=0

We multiply parentheses ..

(+30t^2-20t+21t-14)=0

We get rid of parentheses

30t^2-20t+21t-14=0

We add all the numbers together, and all the variables

30t^2+t-14=0

a = 30; b = 1; c = -14;
Δ = b2-4ac
Δ = 12-4·30·(-14)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-41}{2*30}=\frac{-42}{60}
=-7/10
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+41}{2*30}=\frac{40}{60}
=2/3
$