2/5x+1=3x-6

Solution for 2/5x+1=3x-6 equation:

2/5x+1=3x-6

We move all terms to the left:

2/5x+1-(3x-6)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

2/5x-3x+6+1=0

We multiply all the terms by the denominator


-3x*5x+6*5x+1*5x+2=0

Wy multiply elements

-15x^2+30x+5x+2=0

We add all the numbers together, and all the variables

-15x^2+35x+2=0

a = -15; b = 35; c = +2;
Δ = b2-4ac
Δ = 352-4·(-15)·2
Δ = 1345
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-\sqrt{1345}}{2*-15}=\frac{-35-\sqrt{1345}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+\sqrt{1345}}{2*-15}=\frac{-35+\sqrt{1345}}{-30}
$