6/5x+3=-5/10x-3

Solution for 6/5x+3=-5/10x-3 equation:

6/5x+3=-5/10x-3

We move all terms to the left:

6/5x+3-(-5/10x-3)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x-3)!=0

x∈R


We get rid of parentheses

6/5x+5/10x+3+3=0

We calculate fractions


60x/50x^2+25x/50x^2+3+3=0

We add all the numbers together, and all the variables

60x/50x^2+25x/50x^2+6=0

We multiply all the terms by the denominator


60x+25x+6*50x^2=0

We add all the numbers together, and all the variables

85x+6*50x^2=0

Wy multiply elements

300x^2+85x=0

a = 300; b = 85; c = 0;
Δ = b2-4ac
Δ = 852-4·300·0
Δ = 7225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225}=85$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(85)-85}{2*300}=\frac{-170}{600}
=-17/60
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(85)+85}{2*300}=\frac{0}{600}
=0
$