(-4t+6)(7t+8)=0

Solution for (-4t+6)(7t+8)=0 equation:

(-4t+6)(7t+8)=0

We multiply parentheses ..

(-28t^2-32t+42t+48)=0

We get rid of parentheses

-28t^2-32t+42t+48=0

We add all the numbers together, and all the variables

-28t^2+10t+48=0

a = -28; b = 10; c = +48;
Δ = b2-4ac
Δ = 102-4·(-28)·48
Δ = 5476
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5476}=74$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-74}{2*-28}=\frac{-84}{-56}
=1+1/2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+74}{2*-28}=\frac{64}{-56}
=-1+1/7
$