1/2u-2/3=4/5u+1

Solution for 1/2u-2/3=4/5u+1 equation:

1/2u-2/3=4/5u+1

We move all terms to the left:

1/2u-2/3-(4/5u+1)=0


Domain of the equation: 2u!=0

u!=0/2

u!=0

u∈R



Domain of the equation: 5u+1)!=0

u∈R


We get rid of parentheses

1/2u-4/5u-1-2/3=0

We calculate fractions


(-100u^2)/90u^2+45u/90u^2+(-72u)/90u^2-1=0

We multiply all the terms by the denominator


(-100u^2)+45u+(-72u)-1*90u^2=0

Wy multiply elements

(-100u^2)-90u^2+45u+(-72u)=0

We get rid of parentheses

-100u^2-90u^2+45u-72u=0

We add all the numbers together, and all the variables

-190u^2-27u=0

a = -190; b = -27; c = 0;
Δ = b2-4ac
Δ = -272-4·(-190)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-27}{2*-190}=\frac{0}{-380}
=0
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+27}{2*-190}=\frac{54}{-380}
=-27/190
$