3/4t=2t-1

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

3/4t=2t-1

We move all terms to the left:

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


Domain of the equation: 4t!=0

t!=0/4

t!=0

t∈R


We get rid of parentheses

3/4t-2t+1=0

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -8; b = 4; c = +3;
Δ = b2-4ac
Δ = 42-4·(-8)·3
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{7}}{2*-8}=\frac{-4-4\sqrt{7}}{-16}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{7}}{2*-8}=\frac{-4+4\sqrt{7}}{-16}
$