b(26.5+b)=702.25

Solution for b(26.5+b)=702.25 equation:

b(26.5+b)=702.25

We move all terms to the left:

b(26.5+b)-(702.25)=0

We add all the numbers together, and all the variables

b(b+26.5)-(702.25)=0

We add all the numbers together, and all the variables

b(b+26.5)-702.25=0

We multiply parentheses

b^2+26.5b-702.25=0

a = 1; b = 26.5; c = -702.25;
Δ = b2-4ac
Δ = 26.52-4·1·(-702.25)
Δ = 3511.25
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{-(26.5)-\sqrt{3511.25}}{2*1}=\frac{-26.5-\sqrt{3511.25}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26.5)+\sqrt{3511.25}}{2*1}=\frac{-26.5+\sqrt{3511.25}}{2}
$