3-2/9x=1/4x-7

Solution for 3-2/9x=1/4x-7 equation:

3-2/9x=1/4x-7

We move all terms to the left:

3-2/9x-(1/4x-7)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 4x-7)!=0

x∈R


We get rid of parentheses

-2/9x-1/4x+7+3=0

We calculate fractions


(-8x)/36x^2+(-9x)/36x^2+7+3=0

We add all the numbers together, and all the variables

(-8x)/36x^2+(-9x)/36x^2+10=0

We multiply all the terms by the denominator


(-8x)+(-9x)+10*36x^2=0

Wy multiply elements

360x^2+(-8x)+(-9x)=0

We get rid of parentheses

360x^2-8x-9x=0

We add all the numbers together, and all the variables

360x^2-17x=0

a = 360; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·360·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-17}{2*360}=\frac{0}{720}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*360}=\frac{34}{720}
=17/360
$