(3x+4)-2x/(2-5x)-7x=-9/58

Solution for (3x+4)-2x/(2-5x)-7x=-9/58 equation:

(3x+4)-2x/(2-5x)-7x=-9/58

We move all terms to the left:

(3x+4)-2x/(2-5x)-7x-(-9/58)=0


Domain of the equation: (2-5x)!=0

We move all terms containing x to the left, all other terms to the right

-5x!=-2

x!=-2/-5

x!=2/5

x∈R


We add all the numbers together, and all the variables

(3x+4)-2x/(-5x+2)-7x-(-9/58)=0

We add all the numbers together, and all the variables

-7x+(3x+4)-2x/(-5x+2)-(-9/58)=0

We get rid of parentheses

-7x+3x-2x/(-5x+2)+4+9/58=0

We calculate fractions


-7x+3x+(-116x)/(-290x+116)+(-45x+18)/(-290x+116)+4=0

We add all the numbers together, and all the variables

-4x+(-116x)/(-290x+116)+(-45x+18)/(-290x+116)+4=0

We multiply all the terms by the denominator


-4x*(-290x+116)+(-116x)+(-45x+18)+4*(-290x+116)=0

We multiply parentheses

1160x^2-464x+(-116x)+(-45x+18)-1160x+464=0

We get rid of parentheses

1160x^2-464x-116x-45x-1160x+18+464=0

We add all the numbers together, and all the variables

1160x^2-1785x+482=0

a = 1160; b = -1785; c = +482;
Δ = b2-4ac
Δ = -17852-4·1160·482
Δ = 949745
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1785)-\sqrt{949745}}{2*1160}=\frac{1785-\sqrt{949745}}{2320}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1785)+\sqrt{949745}}{2*1160}=\frac{1785+\sqrt{949745}}{2320}
$