4/5u-7/2=-1/2u-7

Solution for 4/5u-7/2=-1/2u-7 equation:

4/5u-7/2=-1/2u-7

We move all terms to the left:

4/5u-7/2-(-1/2u-7)=0


Domain of the equation: 5u!=0

u!=0/5

u!=0

u∈R



Domain of the equation: 2u-7)!=0

u∈R


We get rid of parentheses

4/5u+1/2u+7-7/2=0

We calculate fractions


32u/40u^2+5u/40u^2+(-35u)/40u^2+7=0

We multiply all the terms by the denominator


32u+5u+(-35u)+7*40u^2=0

We add all the numbers together, and all the variables

37u+(-35u)+7*40u^2=0

Wy multiply elements

280u^2+37u+(-35u)=0

We get rid of parentheses

280u^2+37u-35u=0

We add all the numbers together, and all the variables

280u^2+2u=0

a = 280; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·280·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*280}=\frac{-4}{560}
=-1/140
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*280}=\frac{0}{560}
=0
$