10+b/6+b(b=12)

Solution for 10+b/6+b(b=12) equation:

10+b/6+b(b=12)

We move all terms to the left:

10+b/6+b(b-(12))=0

We multiply parentheses

b^2+b/6-12b+10=0

We multiply all the terms by the denominator


b^2*6+b-12b*6+10*6=0

We add all the numbers together, and all the variables

b^2*6+b-12b*6+60=0

Wy multiply elements

6b^2+b-72b+60=0

We add all the numbers together, and all the variables

6b^2-71b+60=0

a = 6; b = -71; c = +60;
Δ = b2-4ac
Δ = -712-4·6·60
Δ = 3601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-71)-\sqrt{3601}}{2*6}=\frac{71-\sqrt{3601}}{12}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-71)+\sqrt{3601}}{2*6}=\frac{71+\sqrt{3601}}{12}
$