0.4x+3=-1/3x-5

Solution for 0.4x+3=-1/3x-5 equation:

0.4x+3=-1/3x-5

We move all terms to the left:

0.4x+3-(-1/3x-5)=0


Domain of the equation: 3x-5)!=0

x∈R


We get rid of parentheses

0.4x+1/3x+5+3=0

We multiply all the terms by the denominator


(0.4x)*3x+5*3x+3*3x+1=0

We add all the numbers together, and all the variables

(+0.4x)*3x+5*3x+3*3x+1=0

We multiply parentheses

0x^2+5*3x+3*3x+1=0

Wy multiply elements

0x^2+15x+9x+1=0

We add all the numbers together, and all the variables

x^2+24x+1=0

a = 1; b = 24; c = +1;
Δ = b2-4ac
Δ = 242-4·1·1
Δ = 572
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:

$\sqrt{\Delta}=\sqrt{572}=\sqrt{4*143}=\sqrt{4}*\sqrt{143}=2\sqrt{143}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{143}}{2*1}=\frac{-24-2\sqrt{143}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{143}}{2*1}=\frac{-24+2\sqrt{143}}{2}
$