2/3x-7+3x=10x+1

Solution for 2/3x-7+3x=10x+1 equation:

2/3x-7+3x=10x+1

We move all terms to the left:

2/3x-7+3x-(10x+1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

3x+2/3x-(10x+1)-7=0

We get rid of parentheses

3x+2/3x-10x-1-7=0

We multiply all the terms by the denominator


3x*3x-10x*3x-1*3x-7*3x+2=0

Wy multiply elements

9x^2-30x^2-3x-21x+2=0

We add all the numbers together, and all the variables

-21x^2-24x+2=0

a = -21; b = -24; c = +2;
Δ = b2-4ac
Δ = -242-4·(-21)·2
Δ = 744
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:

$\sqrt{\Delta}=\sqrt{744}=\sqrt{4*186}=\sqrt{4}*\sqrt{186}=2\sqrt{186}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{186}}{2*-21}=\frac{24-2\sqrt{186}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{186}}{2*-21}=\frac{24+2\sqrt{186}}{-42}
$