3/4+b(3/4)=21

Solution for 3/4+b(3/4)=21 equation:

3/4+b(3/4)=21

We move all terms to the left:

3/4+b(3/4)-(21)=0

determiningTheFunctionDomain
b(3/4)-21+3/4=0

We add all the numbers together, and all the variables

b(+3/4)-21+3/4=0

We multiply parentheses

3b^2-21+3/4=0

We multiply all the terms by the denominator


3b^2*4+3-21*4=0

We add all the numbers together, and all the variables

3b^2*4-81=0

Wy multiply elements

12b^2-81=0

a = 12; b = 0; c = -81;
Δ = b2-4ac
Δ = 02-4·12·(-81)
Δ = 3888
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:

$\sqrt{\Delta}=\sqrt{3888}=\sqrt{1296*3}=\sqrt{1296}*\sqrt{3}=36\sqrt{3}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{3}}{2*12}=\frac{0-36\sqrt{3}}{24}
=-\frac{36\sqrt{3}}{24}
=-\frac{3\sqrt{3}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{3}}{2*12}=\frac{0+36\sqrt{3}}{24}
=\frac{36\sqrt{3}}{24}
=\frac{3\sqrt{3}}{2}
$