30=1/2*b*12

Solution for 30=1/2*b*12 equation:

30=1/2*b*12

We move all terms to the left:

30-(1/2*b*12)=0


Domain of the equation: 2*b*12)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

-(+1/2*b*12)+30=0

We get rid of parentheses

-1/2*b*12+30=0

We multiply all the terms by the denominator


30*2*b*12-1=0

Wy multiply elements

720b*b-1=0

Wy multiply elements

720b^2-1=0

a = 720; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·720·(-1)
Δ = 2880
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:

$\sqrt{\Delta}=\sqrt{2880}=\sqrt{576*5}=\sqrt{576}*\sqrt{5}=24\sqrt{5}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{5}}{2*720}=\frac{0-24\sqrt{5}}{1440}
=-\frac{24\sqrt{5}}{1440}
=-\frac{\sqrt{5}}{60}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{5}}{2*720}=\frac{0+24\sqrt{5}}{1440}
=\frac{24\sqrt{5}}{1440}
=\frac{\sqrt{5}}{60}
$