-4t(-3t+1)-7t=5t-4

Solution for -4t(-3t+1)-7t=5t-4 equation:

-4t(-3t+1)-7t=5t-4

We move all terms to the left:

-4t(-3t+1)-7t-(5t-4)=0

We add all the numbers together, and all the variables

-7t-4t(-3t+1)-(5t-4)=0

We multiply parentheses

12t^2-7t-4t-(5t-4)=0

We get rid of parentheses

12t^2-7t-4t-5t+4=0

We add all the numbers together, and all the variables

12t^2-16t+4=0

a = 12; b = -16; c = +4;
Δ = b2-4ac
Δ = -162-4·12·4
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8}{2*12}=\frac{8}{24}
=1/3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8}{2*12}=\frac{24}{24}
=1
$