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

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

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

We move all terms to the left:

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


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 5x+6)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-15x)/50x^2+60x/50x^2-6+3=0

We add all the numbers together, and all the variables

(-15x)/50x^2+60x/50x^2-3=0

We multiply all the terms by the denominator


(-15x)+60x-3*50x^2=0

We add all the numbers together, and all the variables

60x+(-15x)-3*50x^2=0

Wy multiply elements

-150x^2+60x+(-15x)=0

We get rid of parentheses

-150x^2+60x-15x=0

We add all the numbers together, and all the variables

-150x^2+45x=0

a = -150; b = 45; c = 0;
Δ = b2-4ac
Δ = 452-4·(-150)·0
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-45}{2*-150}=\frac{-90}{-300}
=3/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+45}{2*-150}=\frac{0}{-300}
=0
$