7/15x=x-2

Solution for 7/15x=x-2 equation:

7/15x=x-2

We move all terms to the left:

7/15x-(x-2)=0


Domain of the equation: 15x!=0

x!=0/15

x!=0

x∈R


We get rid of parentheses

7/15x-x+2=0

We multiply all the terms by the denominator


-x*15x+2*15x+7=0

Wy multiply elements

-15x^2+30x+7=0

a = -15; b = 30; c = +7;
Δ = b2-4ac
Δ = 302-4·(-15)·7
Δ = 1320
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:

$\sqrt{\Delta}=\sqrt{1320}=\sqrt{4*330}=\sqrt{4}*\sqrt{330}=2\sqrt{330}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{330}}{2*-15}=\frac{-30-2\sqrt{330}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{330}}{2*-15}=\frac{-30+2\sqrt{330}}{-30}
$