x+2=7/5x

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

x+2=7/5x

We move all terms to the left:

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


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

x-7/5x+2=0

We multiply all the terms by the denominator


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

Wy multiply elements

5x^2+10x-7=0

a = 5; b = 10; c = -7;
Δ = b2-4ac
Δ = 102-4·5·(-7)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4\sqrt{15}}{2*5}=\frac{-10-4\sqrt{15}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4\sqrt{15}}{2*5}=\frac{-10+4\sqrt{15}}{10}
$