5/2u-7/3=-3/4u-2

Solution for 5/2u-7/3=-3/4u-2 equation:

5/2u-7/3=-3/4u-2

We move all terms to the left:

5/2u-7/3-(-3/4u-2)=0


Domain of the equation: 2u!=0

u!=0/2

u!=0

u∈R



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

u∈R


We get rid of parentheses

5/2u+3/4u+2-7/3=0

We calculate fractions


(-224u^2)/72u^2+180u/72u^2+54u/72u^2+2=0

We multiply all the terms by the denominator


(-224u^2)+180u+54u+2*72u^2=0

We add all the numbers together, and all the variables

(-224u^2)+234u+2*72u^2=0

Wy multiply elements

(-224u^2)+144u^2+234u=0

We get rid of parentheses

-224u^2+144u^2+234u=0

We add all the numbers together, and all the variables

-80u^2+234u=0

a = -80; b = 234; c = 0;
Δ = b2-4ac
Δ = 2342-4·(-80)·0
Δ = 54756
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{54756}=234$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(234)-234}{2*-80}=\frac{-468}{-160}
=2+37/40
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(234)+234}{2*-80}=\frac{0}{-160}
=0
$