12+2/5u=1/2u+4

Solution for 12+2/5u=1/2u+4 equation:

12+2/5u=1/2u+4

We move all terms to the left:

12+2/5u-(1/2u+4)=0


Domain of the equation: 5u!=0

u!=0/5

u!=0

u∈R



Domain of the equation: 2u+4)!=0

u∈R


We get rid of parentheses

2/5u-1/2u-4+12=0

We calculate fractions


4u/10u^2+(-5u)/10u^2-4+12=0

We add all the numbers together, and all the variables

4u/10u^2+(-5u)/10u^2+8=0

We multiply all the terms by the denominator


4u+(-5u)+8*10u^2=0

Wy multiply elements

80u^2+4u+(-5u)=0

We get rid of parentheses

80u^2+4u-5u=0

We add all the numbers together, and all the variables

80u^2-1u=0

a = 80; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·80·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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