(12/5)x=4-x

Solution for (12/5)x=4-x equation:

(12/5)x=4-x

We move all terms to the left:

(12/5)x-(4-x)=0


Domain of the equation: 5)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+12/5)x-(-1x+4)=0

We multiply parentheses

12x^2-(-1x+4)=0

We get rid of parentheses

12x^2+1x-4=0

We add all the numbers together, and all the variables

12x^2+x-4=0

a = 12; b = 1; c = -4;
Δ = b2-4ac
Δ = 12-4·12·(-4)
Δ = 193
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{-(1)-\sqrt{193}}{2*12}=\frac{-1-\sqrt{193}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{193}}{2*12}=\frac{-1+\sqrt{193}}{24}
$