9t^2-10t=3t^2-4

Solution for 9t^2-10t=3t^2-4 equation:

9t^2-10t=3t^2-4

We move all terms to the left:

9t^2-10t-(3t^2-4)=0

We get rid of parentheses

9t^2-3t^2-10t+4=0

We add all the numbers together, and all the variables

6t^2-10t+4=0

a = 6; b = -10; c = +4;
Δ = b2-4ac
Δ = -102-4·6·4
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2}{2*6}=\frac{8}{12}
=2/3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2}{2*6}=\frac{12}{12}
=1
$