8+6b(b=7)

Solution for 8+6b(b=7) equation:

8+6b(b=7)

We move all terms to the left:

8+6b(b-(7))=0

We multiply parentheses

6b^2-42b+8=0

a = 6; b = -42; c = +8;
Δ = b2-4ac
Δ = -422-4·6·8
Δ = 1572
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:

$\sqrt{\Delta}=\sqrt{1572}=\sqrt{4*393}=\sqrt{4}*\sqrt{393}=2\sqrt{393}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{393}}{2*6}=\frac{42-2\sqrt{393}}{12}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{393}}{2*6}=\frac{42+2\sqrt{393}}{12}
$