2/5x-3=2x+7

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

2/5x-3=2x+7

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

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

a = -10; b = -50; c = +2;
Δ = b2-4ac
Δ = -502-4·(-10)·2
Δ = 2580
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:

$\sqrt{\Delta}=\sqrt{2580}=\sqrt{4*645}=\sqrt{4}*\sqrt{645}=2\sqrt{645}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{645}}{2*-10}=\frac{50-2\sqrt{645}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{645}}{2*-10}=\frac{50+2\sqrt{645}}{-20}
$