b(1.75b)2=34705779

Solution for b(1.75b)2=34705779 equation:

b(1.75b)2=34705779

We move all terms to the left:

b(1.75b)2-(34705779)=0

We add all the numbers together, and all the variables

b(+1.75b)2-34705779=0

We multiply parentheses

2b^2-34705779=0

a = 2; b = 0; c = -34705779;
Δ = b2-4ac
Δ = 02-4·2·(-34705779)
Δ = 277646232
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:

$\sqrt{\Delta}=\sqrt{277646232}=\sqrt{4*69411558}=\sqrt{4}*\sqrt{69411558}=2\sqrt{69411558}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{69411558}}{2*2}=\frac{0-2\sqrt{69411558}}{4}
=-\frac{2\sqrt{69411558}}{4}
=-\frac{\sqrt{69411558}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{69411558}}{2*2}=\frac{0+2\sqrt{69411558}}{4}
=\frac{2\sqrt{69411558}}{4}
=\frac{\sqrt{69411558}}{2}
$