2x+7)/9=4x-1)/5

Solution for 2x+7)/9=4x-1)/5 equation:

2x+7)/9=4x-1)/5

We move all terms to the left:

2x+7)/9-(4x-1)/5)=0


Domain of the equation: 9-(4x!=0

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

-(4x!=-9

x∈R


We calculate fractions


2x+()/(-20x+9)-4x/(-20x+9)+(-1)*9=0

We add all the numbers together, and all the variables

2x+()/(-20x+9)-4x/(-20x+9)-9=0

We multiply all the terms by the denominator


2x*(-20x+9)-4x-9*(-20x+9)+()=0

We add all the numbers together, and all the variables

-4x+2x*(-20x+9)-9*(-20x+9)=0

We multiply parentheses

-40x^2-4x+18x+180x-81=0

We add all the numbers together, and all the variables

-40x^2+194x-81=0

a = -40; b = 194; c = -81;
Δ = b2-4ac
Δ = 1942-4·(-40)·(-81)
Δ = 24676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{24676}=\sqrt{4*6169}=\sqrt{4}*\sqrt{6169}=2\sqrt{6169}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(194)-2\sqrt{6169}}{2*-40}=\frac{-194-2\sqrt{6169}}{-80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(194)+2\sqrt{6169}}{2*-40}=\frac{-194+2\sqrt{6169}}{-80}
$