1/10u-3/4=2/3u+1

Solution for 1/10u-3/4=2/3u+1 equation:

1/10u-3/4=2/3u+1

We move all terms to the left:

1/10u-3/4-(2/3u+1)=0


Domain of the equation: 10u!=0

u!=0/10

u!=0

u∈R



Domain of the equation: 3u+1)!=0

u∈R


We get rid of parentheses

1/10u-2/3u-1-3/4=0

We calculate fractions


(-270u^2)/480u^2+48u/480u^2+(-320u)/480u^2-1=0

We multiply all the terms by the denominator


(-270u^2)+48u+(-320u)-1*480u^2=0

Wy multiply elements

(-270u^2)-480u^2+48u+(-320u)=0

We get rid of parentheses

-270u^2-480u^2+48u-320u=0

We add all the numbers together, and all the variables

-750u^2-272u=0

a = -750; b = -272; c = 0;
Δ = b2-4ac
Δ = -2722-4·(-750)·0
Δ = 73984
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{73984}=272$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-272)-272}{2*-750}=\frac{0}{-1500}
=0
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-272)+272}{2*-750}=\frac{544}{-1500}
=-136/375
$