b1+b2/2=30+8/2

Solution for b1+b2/2=30+8/2 equation:

b1+b2/2=30+8/2

We move all terms to the left:

b1+b2/2-(30+8/2)=0

We add all the numbers together, and all the variables

b1+b2/2-34=0

We add all the numbers together, and all the variables

b+b2/2-34=0

We multiply all the terms by the denominator


b*2+b2-34*2=0

We add all the numbers together, and all the variables

b^2+b*2-68=0

Wy multiply elements

b^2+2b-68=0

a = 1; b = 2; c = -68;
Δ = b2-4ac
Δ = 22-4·1·(-68)
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{69}}{2*1}=\frac{-2-2\sqrt{69}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{69}}{2*1}=\frac{-2+2\sqrt{69}}{2}
$