b+3/4b=7

Solution for b+3/4b=7 equation:

b+3/4b=7

We move all terms to the left:

b+3/4b-(7)=0


Domain of the equation: 4b!=0

b!=0/4

b!=0

b∈R


We multiply all the terms by the denominator


b*4b-7*4b+3=0

Wy multiply elements

4b^2-28b+3=0

a = 4; b = -28; c = +3;
Δ = b2-4ac
Δ = -282-4·4·3
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{46}}{2*4}=\frac{28-4\sqrt{46}}{8}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{46}}{2*4}=\frac{28+4\sqrt{46}}{8}
$