1/8x+2x+7/8x=-30

Solution for 1/8x+2x+7/8x=-30 equation:

1/8x+2x+7/8x=-30

We move all terms to the left:

1/8x+2x+7/8x-(-30)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

2x+1/8x+7/8x+30=0

We multiply all the terms by the denominator


2x*8x+30*8x+1+7=0

We add all the numbers together, and all the variables

2x*8x+30*8x+8=0

Wy multiply elements

16x^2+240x+8=0

a = 16; b = 240; c = +8;
Δ = b2-4ac
Δ = 2402-4·16·8
Δ = 57088
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:

$\sqrt{\Delta}=\sqrt{57088}=\sqrt{256*223}=\sqrt{256}*\sqrt{223}=16\sqrt{223}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-16\sqrt{223}}{2*16}=\frac{-240-16\sqrt{223}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+16\sqrt{223}}{2*16}=\frac{-240+16\sqrt{223}}{32}
$