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

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

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

We move all terms to the left:

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


Domain of the equation: 2t!=0

t!=0/2

t!=0

t∈R



Domain of the equation: 4t-2)!=0

t∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

4t/8t^2+(-6t)/8t^2+5=0

We multiply all the terms by the denominator


4t+(-6t)+5*8t^2=0

Wy multiply elements

40t^2+4t+(-6t)=0

We get rid of parentheses

40t^2+4t-6t=0

We add all the numbers together, and all the variables

40t^2-2t=0

a = 40; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·40·0
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{-(-2)-2}{2*40}=\frac{0}{80}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*40}=\frac{4}{80}
=1/20
$