x+14=3/5x

Solution for x+14=3/5x equation:

x+14=3/5x

We move all terms to the left:

x+14-(3/5x)=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-(+3/5x)+14=0

We get rid of parentheses

x-3/5x+14=0

We multiply all the terms by the denominator


x*5x+14*5x-3=0

Wy multiply elements

5x^2+70x-3=0

a = 5; b = 70; c = -3;
Δ = b2-4ac
Δ = 702-4·5·(-3)
Δ = 4960
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:

$\sqrt{\Delta}=\sqrt{4960}=\sqrt{16*310}=\sqrt{16}*\sqrt{310}=4\sqrt{310}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-4\sqrt{310}}{2*5}=\frac{-70-4\sqrt{310}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+4\sqrt{310}}{2*5}=\frac{-70+4\sqrt{310}}{10}
$