x/11x-3=8x+15

Solution for x/11x-3=8x+15 equation:

x/11x-3=8x+15

We move all terms to the left:

x/11x-3-(8x+15)=0


Domain of the equation: 11x!=0

x!=0/11

x!=0

x∈R


We get rid of parentheses

x/11x-8x-15-3=0

We multiply all the terms by the denominator


x-8x*11x-15*11x-3*11x=0

Wy multiply elements

-88x^2+x-165x-33x=0

We add all the numbers together, and all the variables

-88x^2-197x=0

a = -88; b = -197; c = 0;
Δ = b2-4ac
Δ = -1972-4·(-88)·0
Δ = 38809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{38809}=197$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-197)-197}{2*-88}=\frac{0}{-176}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-197)+197}{2*-88}=\frac{394}{-176}
=-2+21/88
$