51/4*b=12

Solution for 51/4*b=12 equation:

51/4*b=12

We move all terms to the left:

51/4*b-(12)=0


Domain of the equation: 4*b!=0

b!=0/1

b!=0

b∈R


We multiply all the terms by the denominator


-12*4*b+51=0

Wy multiply elements

-48b*b+51=0

Wy multiply elements

-48b^2+51=0

a = -48; b = 0; c = +51;
Δ = b2-4ac
Δ = 02-4·(-48)·51
Δ = 9792
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:

$\sqrt{\Delta}=\sqrt{9792}=\sqrt{576*17}=\sqrt{576}*\sqrt{17}=24\sqrt{17}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{17}}{2*-48}=\frac{0-24\sqrt{17}}{-96}
=-\frac{24\sqrt{17}}{-96}
=-\frac{\sqrt{17}}{-4}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{17}}{2*-48}=\frac{0+24\sqrt{17}}{-96}
=\frac{24\sqrt{17}}{-96}
=\frac{\sqrt{17}}{-4}
$