U-2/u+3=u+3/u-7+1

Solution for U-2/u+3=u+3/u-7+1 equation:

-2/U+3=U+3/U-7+1

We move all terms to the left:

-2/U+3-(U+3/U-7+1)=0


Domain of the equation: U!=0

U∈R



Domain of the equation: U-7+1)!=0

We move all terms containing U to the left, all other terms to the right

U+1)!=7

U∈R


We add all the numbers together, and all the variables

-2/U-(U+3/U-6)+3=0

We get rid of parentheses

-2/U-U-3/U+6+3=0

We multiply all the terms by the denominator


-U*U+6*U+3*U-2-3=0

We add all the numbers together, and all the variables

9U-U*U-5=0

Wy multiply elements

-1U^2+9U-5=0

a = -1; b = 9; c = -5;
Δ = b2-4ac
Δ = 92-4·(-1)·(-5)
Δ = 61
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$U_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$U_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$U_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{61}}{2*-1}=\frac{-9-\sqrt{61}}{-2}
$
$U_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{61}}{2*-1}=\frac{-9+\sqrt{61}}{-2}
$