6/11x+4=1/4x+18

Solution for 6/11x+4=1/4x+18 equation:

6/11x+4=1/4x+18

We move all terms to the left:

6/11x+4-(1/4x+18)=0


Domain of the equation: 11x!=0

x!=0/11

x!=0

x∈R



Domain of the equation: 4x+18)!=0

x∈R


We get rid of parentheses

6/11x-1/4x-18+4=0

We calculate fractions


24x/44x^2+(-11x)/44x^2-18+4=0

We add all the numbers together, and all the variables

24x/44x^2+(-11x)/44x^2-14=0

We multiply all the terms by the denominator


24x+(-11x)-14*44x^2=0

Wy multiply elements

-616x^2+24x+(-11x)=0

We get rid of parentheses

-616x^2+24x-11x=0

We add all the numbers together, and all the variables

-616x^2+13x=0

a = -616; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-616)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-616}=\frac{-26}{-1232}
=13/616
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-616}=\frac{0}{-1232}
=0
$