3/5x+1.2=x-4

Solution for 3/5x+1.2=x-4 equation:

3/5x+1.2=x-4

We move all terms to the left:

3/5x+1.2-(x-4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

3/5x-x+4+1.2=0

We multiply all the terms by the denominator


-x*5x+4*5x+(1.2)*5x+3=0

We multiply parentheses

-x*5x+4*5x+6x+3=0

Wy multiply elements

-5x^2+20x+6x+3=0

We add all the numbers together, and all the variables

-5x^2+26x+3=0

a = -5; b = 26; c = +3;
Δ = b2-4ac
Δ = 262-4·(-5)·3
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-4\sqrt{46}}{2*-5}=\frac{-26-4\sqrt{46}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+4\sqrt{46}}{2*-5}=\frac{-26+4\sqrt{46}}{-10}
$