3/5x+7=-x-3

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

3/5x+7=-x-3

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

3/5x-(-1x-3)+7=0

We get rid of parentheses

3/5x+1x+3+7=0

We multiply all the terms by the denominator


1x*5x+3*5x+7*5x+3=0

Wy multiply elements

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

We add all the numbers together, and all the variables

5x^2+50x+3=0

a = 5; b = 50; c = +3;
Δ = b2-4ac
Δ = 502-4·5·3
Δ = 2440
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:

$\sqrt{\Delta}=\sqrt{2440}=\sqrt{4*610}=\sqrt{4}*\sqrt{610}=2\sqrt{610}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{610}}{2*5}=\frac{-50-2\sqrt{610}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{610}}{2*5}=\frac{-50+2\sqrt{610}}{10}
$