-9/14x+18=-2/3x+17

Solution for -9/14x+18=-2/3x+17 equation:

-9/14x+18=-2/3x+17

We move all terms to the left:

-9/14x+18-(-2/3x+17)=0


Domain of the equation: 14x!=0

x!=0/14

x!=0

x∈R



Domain of the equation: 3x+17)!=0

x∈R


We get rid of parentheses

-9/14x+2/3x-17+18=0

We calculate fractions


(-27x)/42x^2+28x/42x^2-17+18=0

We add all the numbers together, and all the variables

(-27x)/42x^2+28x/42x^2+1=0

We multiply all the terms by the denominator


(-27x)+28x+1*42x^2=0

We add all the numbers together, and all the variables

28x+(-27x)+1*42x^2=0

Wy multiply elements

42x^2+28x+(-27x)=0

We get rid of parentheses

42x^2+28x-27x=0

We add all the numbers together, and all the variables

42x^2+x=0

a = 42; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·42·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*42}=\frac{-2}{84}
=-1/42
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*42}=\frac{0}{84}
=0
$