2x-3x+4=-1/3x-10

Solution for 2x-3x+4=-1/3x-10 equation:

2x-3x+4=-1/3x-10

We move all terms to the left:

2x-3x+4-(-1/3x-10)=0


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

x∈R


We add all the numbers together, and all the variables

-1x-(-1/3x-10)+4=0

We get rid of parentheses

-1x+1/3x+10+4=0

We multiply all the terms by the denominator


-1x*3x+10*3x+4*3x+1=0

Wy multiply elements

-3x^2+30x+12x+1=0

We add all the numbers together, and all the variables

-3x^2+42x+1=0

a = -3; b = 42; c = +1;
Δ = b2-4ac
Δ = 422-4·(-3)·1
Δ = 1776
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:

$\sqrt{\Delta}=\sqrt{1776}=\sqrt{16*111}=\sqrt{16}*\sqrt{111}=4\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-4\sqrt{111}}{2*-3}=\frac{-42-4\sqrt{111}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+4\sqrt{111}}{2*-3}=\frac{-42+4\sqrt{111}}{-6}
$