3/5x+3=x+7

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

3/5x+3=x+7

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-5x^2-35x+15x+3=0

We add all the numbers together, and all the variables

-5x^2-20x+3=0

a = -5; b = -20; c = +3;
Δ = b2-4ac
Δ = -202-4·(-5)·3
Δ = 460
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:

$\sqrt{\Delta}=\sqrt{460}=\sqrt{4*115}=\sqrt{4}*\sqrt{115}=2\sqrt{115}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{115}}{2*-5}=\frac{20-2\sqrt{115}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{115}}{2*-5}=\frac{20+2\sqrt{115}}{-10}
$