(6x^2/6x+6)+(5x/5x+5)-6=0

Solution for (6x^2/6x+6)+(5x/5x+5)-6=0 equation:

(6x^2/6x+6)+(5x/5x+5)-6=0


Domain of the equation: 6x+6)!=0

x∈R



Domain of the equation: 5x+5)!=0

x∈R


We get rid of parentheses

6x^2/6x+5x/5x+6+5-6=0

Fractions to decimals

6x^2/6x+6+5-6+1=0

We multiply all the terms by the denominator


6x^2+6*6x+5*6x-6*6x+1*6x=0

Wy multiply elements

6x^2+36x+30x-36x+6x=0

We add all the numbers together, and all the variables

6x^2+36x=0

a = 6; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·6·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*6}=\frac{-72}{12}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*6}=\frac{0}{12}
=0
$