X/5x+2x-4=4x+5

Solution for X/5x+2x-4=4x+5 equation:

X/5X+2X-4=4X+5

We move all terms to the left:

X/5X+2X-4-(4X+5)=0


Domain of the equation: 5X!=0

X!=0/5

X!=0

X∈R


We add all the numbers together, and all the variables

2X+X/5X-(4X+5)-4=0

We get rid of parentheses

2X+X/5X-4X-5-4=0

We multiply all the terms by the denominator


2X*5X+X-4X*5X-5*5X-4*5X=0

We add all the numbers together, and all the variables

X+2X*5X-4X*5X-5*5X-4*5X=0

Wy multiply elements

10X^2-20X^2+X-25X-20X=0

We add all the numbers together, and all the variables

-10X^2-44X=0

a = -10; b = -44; c = 0;
Δ = b2-4ac
Δ = -442-4·(-10)·0
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-44}{2*-10}=\frac{0}{-20}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+44}{2*-10}=\frac{88}{-20}
=-4+2/5
$