X/4x+4=-1x+9

Solution for X/4x+4=-1x+9 equation:

X/4X+4=-1X+9

We move all terms to the left:

X/4X+4-(-1X+9)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We get rid of parentheses

X/4X+1X-9+4=0

We multiply all the terms by the denominator


X+1X*4X-9*4X+4*4X=0

Wy multiply elements

4X^2+X-36X+16X=0

We add all the numbers together, and all the variables

4X^2-19X=0

a = 4; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·4·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*4}=\frac{0}{8}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*4}=\frac{38}{8}
=4+3/4
$