-1/2b+4b=6

Solution for -1/2b+4b=6 equation:

-1/2b+4b=6

We move all terms to the left:

-1/2b+4b-(6)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


We add all the numbers together, and all the variables

4b-1/2b-6=0

We multiply all the terms by the denominator


4b*2b-6*2b-1=0

Wy multiply elements

8b^2-12b-1=0

a = 8; b = -12; c = -1;
Δ = b2-4ac
Δ = -122-4·8·(-1)
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{11}}{2*8}=\frac{12-4\sqrt{11}}{16}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{11}}{2*8}=\frac{12+4\sqrt{11}}{16}
$