2+8x=1/5x-7

Solution for 2+8x=1/5x-7 equation:

2+8x=1/5x-7

We move all terms to the left:

2+8x-(1/5x-7)=0


Domain of the equation: 5x-7)!=0

x∈R


We get rid of parentheses

8x-1/5x+7+2=0

We multiply all the terms by the denominator


8x*5x+7*5x+2*5x-1=0

Wy multiply elements

40x^2+35x+10x-1=0

We add all the numbers together, and all the variables

40x^2+45x-1=0

a = 40; b = 45; c = -1;
Δ = b2-4ac
Δ = 452-4·40·(-1)
Δ = 2185
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-\sqrt{2185}}{2*40}=\frac{-45-\sqrt{2185}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{2185}}{2*40}=\frac{-45+\sqrt{2185}}{80}
$