-2/3u-7/2=1/2u-5

Solution for -2/3u-7/2=1/2u-5 equation:

-2/3u-7/2=1/2u-5

We move all terms to the left:

-2/3u-7/2-(1/2u-5)=0


Domain of the equation: 3u!=0

u!=0/3

u!=0

u∈R



Domain of the equation: 2u-5)!=0

u∈R


We get rid of parentheses

-2/3u-1/2u+5-7/2=0

We calculate fractions


(-16u)/24u^2+(-3u)/24u^2+(-21u)/24u^2+5=0

We multiply all the terms by the denominator


(-16u)+(-3u)+(-21u)+5*24u^2=0

Wy multiply elements

120u^2+(-16u)+(-3u)+(-21u)=0

We get rid of parentheses

120u^2-16u-3u-21u=0

We add all the numbers together, and all the variables

120u^2-40u=0

a = 120; b = -40; c = 0;
Δ = b2-4ac
Δ = -402-4·120·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-40}{2*120}=\frac{0}{240}
=0
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40}{2*120}=\frac{80}{240}
=1/3
$