b2=16/120

Solution for b2=16/120 equation:

b2=16/120

We move all terms to the left:

b2-(16/120)=0

We add all the numbers together, and all the variables

b2-(+16/120)=0

We add all the numbers together, and all the variables

b^2-(+16/120)=0

We get rid of parentheses

b^2-16/120=0

We multiply all the terms by the denominator


b^2*120-16=0

Wy multiply elements

120b^2-16=0

a = 120; b = 0; c = -16;
Δ = b2-4ac
Δ = 02-4·120·(-16)
Δ = 7680
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:

$\sqrt{\Delta}=\sqrt{7680}=\sqrt{256*30}=\sqrt{256}*\sqrt{30}=16\sqrt{30}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{30}}{2*120}=\frac{0-16\sqrt{30}}{240}
=-\frac{16\sqrt{30}}{240}
=-\frac{\sqrt{30}}{15}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{30}}{2*120}=\frac{0+16\sqrt{30}}{240}
=\frac{16\sqrt{30}}{240}
=\frac{\sqrt{30}}{15}
$