4x-84=1/8x+9

Solution for 4x-84=1/8x+9 equation:

4x-84=1/8x+9

We move all terms to the left:

4x-84-(1/8x+9)=0


Domain of the equation: 8x+9)!=0

x∈R


We get rid of parentheses

4x-1/8x-9-84=0

We multiply all the terms by the denominator


4x*8x-9*8x-84*8x-1=0

Wy multiply elements

32x^2-72x-672x-1=0

We add all the numbers together, and all the variables

32x^2-744x-1=0

a = 32; b = -744; c = -1;
Δ = b2-4ac
Δ = -7442-4·32·(-1)
Δ = 553664
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:

$\sqrt{\Delta}=\sqrt{553664}=\sqrt{64*8651}=\sqrt{64}*\sqrt{8651}=8\sqrt{8651}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-744)-8\sqrt{8651}}{2*32}=\frac{744-8\sqrt{8651}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-744)+8\sqrt{8651}}{2*32}=\frac{744+8\sqrt{8651}}{64}
$