4=12/5x+x

Solution for 4=12/5x+x equation:

4=12/5x+x

We move all terms to the left:

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


Domain of the equation: 5x+x)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-x-12/5x+4=0

We multiply all the terms by the denominator


-x*5x+4*5x-12=0

Wy multiply elements

-5x^2+20x-12=0

a = -5; b = 20; c = -12;
Δ = b2-4ac
Δ = 202-4·(-5)·(-12)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{10}}{2*-5}=\frac{-20-4\sqrt{10}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{10}}{2*-5}=\frac{-20+4\sqrt{10}}{-10}
$