3t^2/4=2t-1

Solution for 3t^2/4=2t-1 equation:

3t^2/4=2t-1

We move all terms to the left:

3t^2/4-(2t-1)=0

We get rid of parentheses

3t^2/4-2t+1=0

We multiply all the terms by the denominator


3t^2-2t*4+1*4=0

We add all the numbers together, and all the variables

3t^2-2t*4+4=0

Wy multiply elements

3t^2-8t+4=0

a = 3; b = -8; c = +4;
Δ = b2-4ac
Δ = -82-4·3·4
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4}{2*3}=\frac{4}{6}
=2/3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4}{2*3}=\frac{12}{6}
=2
$