x2/x-23=-x+11

Solution for x2/x-23=-x+11 equation:

x2/x-23=-x+11

We move all terms to the left:

x2/x-23-(-x+11)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x2/x-(-1x+11)-23=0

We get rid of parentheses

x2/x+1x-11-23=0

We multiply all the terms by the denominator


x2+1x*x-11*x-23*x=0

We add all the numbers together, and all the variables

x^2-34x+1x*x=0

Wy multiply elements

x^2+x^2-34x=0

We add all the numbers together, and all the variables

2x^2-34x=0

a = 2; b = -34; c = 0;
Δ = b2-4ac
Δ = -342-4·2·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-34}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+34}{2*2}=\frac{68}{4}
=17
$