b1+b2/2=30+8/2

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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} $

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