.5b+4=1/8b+88

Solution for .5b+4=1/8b+88 equation:

.5b+4=1/8b+88

We move all terms to the left:

.5b+4-(1/8b+88)=0


Domain of the equation: 8b+88)!=0

b∈R


We get rid of parentheses

.5b-1/8b-88+4=0

We multiply all the terms by the denominator


(.5b)*8b-88*8b+4*8b-1=0

We add all the numbers together, and all the variables

(+.5b)*8b-88*8b+4*8b-1=0

We multiply parentheses

8b^2-88*8b+4*8b-1=0

Wy multiply elements

8b^2-704b+32b-1=0

We add all the numbers together, and all the variables

8b^2-672b-1=0

a = 8; b = -672; c = -1;
Δ = b2-4ac
Δ = -6722-4·8·(-1)
Δ = 451616
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{451616}=\sqrt{16*28226}=\sqrt{16}*\sqrt{28226}=4\sqrt{28226}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-672)-4\sqrt{28226}}{2*8}=\frac{672-4\sqrt{28226}}{16}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-672)+4\sqrt{28226}}{2*8}=\frac{672+4\sqrt{28226}}{16}
$