35=10(b+8)b

Solution for 35=10(b+8)b equation:

35=10(b+8)b

We move all terms to the left:

35-(10(b+8)b)=0


We calculate terms in parentheses: -(10(b+8)b), so:

10(b+8)b

We multiply parentheses

10b^2+80b

Back to the equation:

-(10b^2+80b)


We get rid of parentheses

-10b^2-80b+35=0

a = -10; b = -80; c = +35;
Δ = b2-4ac
Δ = -802-4·(-10)·35
Δ = 7800
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:

$\sqrt{\Delta}=\sqrt{7800}=\sqrt{100*78}=\sqrt{100}*\sqrt{78}=10\sqrt{78}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-10\sqrt{78}}{2*-10}=\frac{80-10\sqrt{78}}{-20}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+10\sqrt{78}}{2*-10}=\frac{80+10\sqrt{78}}{-20}
$