5/2u-7/2=-6/5u-4

Solution for 5/2u-7/2=-6/5u-4 equation:

5/2u-7/2=-6/5u-4

We move all terms to the left:

5/2u-7/2-(-6/5u-4)=0


Domain of the equation: 2u!=0

u!=0/2

u!=0

u∈R



Domain of the equation: 5u-4)!=0

u∈R


We get rid of parentheses

5/2u+6/5u+4-7/2=0

We calculate fractions


25u/40u^2+48u/40u^2+(-35u)/40u^2+4=0

We multiply all the terms by the denominator


25u+48u+(-35u)+4*40u^2=0

We add all the numbers together, and all the variables

73u+(-35u)+4*40u^2=0

Wy multiply elements

160u^2+73u+(-35u)=0

We get rid of parentheses

160u^2+73u-35u=0

We add all the numbers together, and all the variables

160u^2+38u=0

a = 160; b = 38; c = 0;
Δ = b2-4ac
Δ = 382-4·160·0
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-38}{2*160}=\frac{-76}{320}
=-19/80
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+38}{2*160}=\frac{0}{320}
=0
$