-1/2b-3=-7b-16

Solution for -1/2b-3=-7b-16 equation:

-1/2b-3=-7b-16

We move all terms to the left:

-1/2b-3-(-7b-16)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


We get rid of parentheses

-1/2b+7b+16-3=0

We multiply all the terms by the denominator


7b*2b+16*2b-3*2b-1=0

Wy multiply elements

14b^2+32b-6b-1=0

We add all the numbers together, and all the variables

14b^2+26b-1=0

a = 14; b = 26; c = -1;
Δ = b2-4ac
Δ = 262-4·14·(-1)
Δ = 732
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:

$\sqrt{\Delta}=\sqrt{732}=\sqrt{4*183}=\sqrt{4}*\sqrt{183}=2\sqrt{183}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{183}}{2*14}=\frac{-26-2\sqrt{183}}{28}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{183}}{2*14}=\frac{-26+2\sqrt{183}}{28}
$