4(6+4/5b)=(9/10b)4

Solution for 4(6+4/5b)=(9/10b)4 equation:

4(6+4/5b)=(9/10b)4

We move all terms to the left:

4(6+4/5b)-((9/10b)4)=0


Domain of the equation: 5b)!=0

b!=0/1

b!=0

b∈R



Domain of the equation: 10b)4)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

4(4/5b+6)-((+9/10b)4)=0

We multiply parentheses

16b-((+9/10b)4)+24=0

We multiply all the terms by the denominator


16b*10b)4)-((+24*10b)4)+9=0

Wy multiply elements

160b^2+240b=0

a = 160; b = 240; c = 0;
Δ = b2-4ac
Δ = 2402-4·160·0
Δ = 57600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{57600}=240$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-240}{2*160}=\frac{-480}{320}
=-1+1/2
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+240}{2*160}=\frac{0}{320}
=0
$