x/4x+3(x-2)=22*

Solution for x/4x+3(x-2)=22* equation:

x/4x+3(x-2)=22*

We move all terms to the left:

x/4x+3(x-2)-(22*)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

x/4x+3(x-2)-0=0

We add all the numbers together, and all the variables

x/4x+3(x-2)=0

We multiply parentheses

x/4x+3x-6=0

We multiply all the terms by the denominator


x+3x*4x-6*4x=0

Wy multiply elements

12x^2+x-24x=0

We add all the numbers together, and all the variables

12x^2-23x=0

a = 12; b = -23; c = 0;
Δ = b2-4ac
Δ = -232-4·12·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-23}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+23}{2*12}=\frac{46}{24}
=1+11/12
$