4t(t-2)=6-3t

Solution for 4t(t-2)=6-3t equation:

4t(t-2)=6-3t

We move all terms to the left:

4t(t-2)-(6-3t)=0

We add all the numbers together, and all the variables

4t(t-2)-(-3t+6)=0

We multiply parentheses

4t^2-8t-(-3t+6)=0

We get rid of parentheses

4t^2-8t+3t-6=0

We add all the numbers together, and all the variables

4t^2-5t-6=0

a = 4; b = -5; c = -6;
Δ = b2-4ac
Δ = -52-4·4·(-6)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-11}{2*4}=\frac{-6}{8}
=-3/4
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+11}{2*4}=\frac{16}{8}
=2
$