15-(1/2)b=-3

Solution for 15-(1/2)b=-3 equation:

15-(1/2)b=-3

We move all terms to the left:

15-(1/2)b-(-3)=0


Domain of the equation: 2)b!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

-(+1/2)b+15-(-3)=0

We add all the numbers together, and all the variables

-(+1/2)b+18=0

We multiply parentheses

-b^2+18=0

We add all the numbers together, and all the variables

-1b^2+18=0

a = -1; b = 0; c = +18;
Δ = b2-4ac
Δ = 02-4·(-1)·18
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{2}}{2*-1}=\frac{0-6\sqrt{2}}{-2}
=-\frac{6\sqrt{2}}{-2}
=-\frac{3\sqrt{2}}{-1}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{2}}{2*-1}=\frac{0+6\sqrt{2}}{-2}
=\frac{6\sqrt{2}}{-2}
=\frac{3\sqrt{2}}{-1}
$