1/8x+x=90

Solution for 1/8x+x=90 equation:

1/8x+x=90

We move all terms to the left:

1/8x+x-(90)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

x+1/8x-90=0

We multiply all the terms by the denominator


x*8x-90*8x+1=0

Wy multiply elements

8x^2-720x+1=0

a = 8; b = -720; c = +1;
Δ = b2-4ac
Δ = -7202-4·8·1
Δ = 518368
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:

$\sqrt{\Delta}=\sqrt{518368}=\sqrt{16*32398}=\sqrt{16}*\sqrt{32398}=4\sqrt{32398}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-720)-4\sqrt{32398}}{2*8}=\frac{720-4\sqrt{32398}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-720)+4\sqrt{32398}}{2*8}=\frac{720+4\sqrt{32398}}{16}
$