8b-3/2b=5

Solution for 8b-3/2b=5 equation:

8b-3/2b=5

We move all terms to the left:

8b-3/2b-(5)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


We multiply all the terms by the denominator


8b*2b-5*2b-3=0

Wy multiply elements

16b^2-10b-3=0

a = 16; b = -10; c = -3;
Δ = b2-4ac
Δ = -102-4·16·(-3)
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{73}}{2*16}=\frac{10-2\sqrt{73}}{32}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{73}}{2*16}=\frac{10+2\sqrt{73}}{32}
$