x+7/8x=90

Solution for x+7/8x=90 equation:

x+7/8x=90

We move all terms to the left:

x+7/8x-(90)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We multiply all the terms by the denominator


x*8x-90*8x+7=0

Wy multiply elements

8x^2-720x+7=0

a = 8; b = -720; c = +7;
Δ = b2-4ac
Δ = -7202-4·8·7
Δ = 518176
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:

$\sqrt{\Delta}=\sqrt{518176}=\sqrt{16*32386}=\sqrt{16}*\sqrt{32386}=4\sqrt{32386}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-720)-4\sqrt{32386}}{2*8}=\frac{720-4\sqrt{32386}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-720)+4\sqrt{32386}}{2*8}=\frac{720+4\sqrt{32386}}{16}
$