-3t(4t-4)+7t=5t-7

Solution for -3t(4t-4)+7t=5t-7 equation:

-3t(4t-4)+7t=5t-7

We move all terms to the left:

-3t(4t-4)+7t-(5t-7)=0

We add all the numbers together, and all the variables

7t-3t(4t-4)-(5t-7)=0

We multiply parentheses

-12t^2+7t+12t-(5t-7)=0

We get rid of parentheses

-12t^2+7t+12t-5t+7=0

We add all the numbers together, and all the variables

-12t^2+14t+7=0

a = -12; b = 14; c = +7;
Δ = b2-4ac
Δ = 142-4·(-12)·7
Δ = 532
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{532}=\sqrt{4*133}=\sqrt{4}*\sqrt{133}=2\sqrt{133}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{133}}{2*-12}=\frac{-14-2\sqrt{133}}{-24}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{133}}{2*-12}=\frac{-14+2\sqrt{133}}{-24}
$