(2t-5)(7t-6)=0

Solution for (2t-5)(7t-6)=0 equation:

(2t-5)(7t-6)=0

We multiply parentheses ..

(+14t^2-12t-35t+30)=0

We get rid of parentheses

14t^2-12t-35t+30=0

We add all the numbers together, and all the variables

14t^2-47t+30=0

a = 14; b = -47; c = +30;
Δ = b2-4ac
Δ = -472-4·14·30
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-23}{2*14}=\frac{24}{28}
=6/7
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+23}{2*14}=\frac{70}{28}
=2+1/2
$