7/8x+8=216;x=1823

Solution for 7/8x+8=216;x=1823 equation:

7/8x+8=216x=1823

We move all terms to the left:

7/8x+8-(216x)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

-216x+7/8x+8=0

We multiply all the terms by the denominator


-216x*8x+8*8x+7=0

Wy multiply elements

-1728x^2+64x+7=0

a = -1728; b = 64; c = +7;
Δ = b2-4ac
Δ = 642-4·(-1728)·7
Δ = 52480
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:

$\sqrt{\Delta}=\sqrt{52480}=\sqrt{256*205}=\sqrt{256}*\sqrt{205}=16\sqrt{205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-16\sqrt{205}}{2*-1728}=\frac{-64-16\sqrt{205}}{-3456}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+16\sqrt{205}}{2*-1728}=\frac{-64+16\sqrt{205}}{-3456}
$