7/5x-9=-x-15

Solution for 7/5x-9=-x-15 equation:

7/5x-9=-x-15

We move all terms to the left:

7/5x-9-(-x-15)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

7/5x-(-1x-15)-9=0

We get rid of parentheses

7/5x+1x+15-9=0

We multiply all the terms by the denominator


1x*5x+15*5x-9*5x+7=0

Wy multiply elements

5x^2+75x-45x+7=0

We add all the numbers together, and all the variables

5x^2+30x+7=0

a = 5; b = 30; c = +7;
Δ = b2-4ac
Δ = 302-4·5·7
Δ = 760
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:

$\sqrt{\Delta}=\sqrt{760}=\sqrt{4*190}=\sqrt{4}*\sqrt{190}=2\sqrt{190}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{190}}{2*5}=\frac{-30-2\sqrt{190}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{190}}{2*5}=\frac{-30+2\sqrt{190}}{10}
$