(3u^2+2)/u=7

Solution for (3u^2+2)/u=7 equation:

(3u^2+2)/u=7

We move all terms to the left:

(3u^2+2)/u-(7)=0


Domain of the equation: u!=0

u∈R


We multiply all the terms by the denominator


(3u^2+2)-7*u=0

We add all the numbers together, and all the variables

-7u+(3u^2+2)=0

We get rid of parentheses

3u^2-7u+2=0

a = 3; b = -7; c = +2;
Δ = b2-4ac
Δ = -72-4·3·2
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-5}{2*3}=\frac{2}{6}
=1/3
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+5}{2*3}=\frac{12}{6}
=2
$