/6x+8=9x+13

Solution for /6x+8=9x+13 equation:

/6x+8=9x+13

We move all terms to the left:

/6x+8-(9x+13)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

/6x-9x-13+8=0

We multiply all the terms by the denominator


-9x*6x-13*6x+8*6x+=0

We add all the numbers together, and all the variables

-9x*6x-13*6x+8*6x=0

Wy multiply elements

-54x^2-78x+48x=0

We add all the numbers together, and all the variables

-54x^2-30x=0

a = -54; b = -30; c = 0;
Δ = b2-4ac
Δ = -302-4·(-54)·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30}{2*-54}=\frac{0}{-108}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30}{2*-54}=\frac{60}{-108}
=-5/9
$