5/2t+7/2=3/4t+14

Solution for 5/2t+7/2=3/4t+14 equation:

5/2t+7/2=3/4t+14

We move all terms to the left:

5/2t+7/2-(3/4t+14)=0


Domain of the equation: 2t!=0

t!=0/2

t!=0

t∈R



Domain of the equation: 4t+14)!=0

t∈R


We get rid of parentheses

5/2t-3/4t-14+7/2=0

We calculate fractions


20t/32t^2+(-24t)/32t^2+28t/32t^2-14=0

We multiply all the terms by the denominator


20t+(-24t)+28t-14*32t^2=0

We add all the numbers together, and all the variables

48t+(-24t)-14*32t^2=0

Wy multiply elements

-448t^2+48t+(-24t)=0

We get rid of parentheses

-448t^2+48t-24t=0

We add all the numbers together, and all the variables

-448t^2+24t=0

a = -448; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·(-448)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*-448}=\frac{-48}{-896}
=3/56
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*-448}=\frac{0}{-896}
=0
$