-(12/8-b)=-b^2

Solution for -(12/8-b)=-b^2 equation:

-(12/8-b)=-b^2

We move all terms to the left:

-(12/8-b)-(-b^2)=0


Domain of the equation: 8-b)!=0

We move all terms containing b to the left, all other terms to the right

-b)!=-8

b!=-8/1

b!=-8

b∈R


We add all the numbers together, and all the variables

-(-b^2)-(-1b+12/8)=0

We get rid of parentheses

b^2+1b-12/8=0

We multiply all the terms by the denominator


b^2*8+1b*8-12=0

Wy multiply elements

8b^2+8b-12=0

a = 8; b = 8; c = -12;
Δ = b2-4ac
Δ = 82-4·8·(-12)
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{7}}{2*8}=\frac{-8-8\sqrt{7}}{16}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{7}}{2*8}=\frac{-8+8\sqrt{7}}{16}
$