2/5x+3x-2=x+10

Solution for 2/5x+3x-2=x+10 equation:

2/5x+3x-2=x+10

We move all terms to the left:

2/5x+3x-2-(x+10)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

3x+2/5x-(x+10)-2=0

We get rid of parentheses

3x+2/5x-x-10-2=0

We multiply all the terms by the denominator


3x*5x-x*5x-10*5x-2*5x+2=0

Wy multiply elements

15x^2-5x^2-50x-10x+2=0

We add all the numbers together, and all the variables

10x^2-60x+2=0

a = 10; b = -60; c = +2;
Δ = b2-4ac
Δ = -602-4·10·2
Δ = 3520
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:

$\sqrt{\Delta}=\sqrt{3520}=\sqrt{64*55}=\sqrt{64}*\sqrt{55}=8\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-8\sqrt{55}}{2*10}=\frac{60-8\sqrt{55}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+8\sqrt{55}}{2*10}=\frac{60+8\sqrt{55}}{20}
$