u-10=-8+35/u

Solution for u-10=-8+35/u equation:

u-10=-8+35/u

We move all terms to the left:

u-10-(-8+35/u)=0


Domain of the equation: u)!=0

u!=0/1

u!=0

u∈R


We add all the numbers together, and all the variables

u-(35/u-8)-10=0

We get rid of parentheses

u-35/u+8-10=0

We multiply all the terms by the denominator


u*u+8*u-10*u-35=0

We add all the numbers together, and all the variables

-2u+u*u-35=0

Wy multiply elements

u^2-2u-35=0

a = 1; b = -2; c = -35;
Δ = b2-4ac
Δ = -22-4·1·(-35)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-12}{2*1}=\frac{-10}{2}
=-5
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+12}{2*1}=\frac{14}{2}
=7
$