2/5x-7=12/5x-2x+3

Solution for 2/5x-7=12/5x-2x+3 equation:

2/5x-7=12/5x-2x+3

We move all terms to the left:

2/5x-7-(12/5x-2x+3)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 5x-2x+3)!=0

x∈R


We add all the numbers together, and all the variables

2/5x-(-2x+12/5x+3)-7=0

We get rid of parentheses

2/5x+2x-12/5x-3-7=0

We multiply all the terms by the denominator


2x*5x-3*5x-7*5x+2-12=0

We add all the numbers together, and all the variables

2x*5x-3*5x-7*5x-10=0

Wy multiply elements

10x^2-15x-35x-10=0

We add all the numbers together, and all the variables

10x^2-50x-10=0

a = 10; b = -50; c = -10;
Δ = b2-4ac
Δ = -502-4·10·(-10)
Δ = 2900
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:

$\sqrt{\Delta}=\sqrt{2900}=\sqrt{100*29}=\sqrt{100}*\sqrt{29}=10\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{29}}{2*10}=\frac{50-10\sqrt{29}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{29}}{2*10}=\frac{50+10\sqrt{29}}{20}
$