7/6*b=420

Solution for 7/6*b=420 equation:

7/6*b=420

We move all terms to the left:

7/6*b-(420)=0


Domain of the equation: 6*b!=0

b!=0/1

b!=0

b∈R


We multiply all the terms by the denominator


-420*6*b+7=0

Wy multiply elements

-2520b*b+7=0

Wy multiply elements

-2520b^2+7=0

a = -2520; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-2520)·7
Δ = 70560
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:

$\sqrt{\Delta}=\sqrt{70560}=\sqrt{7056*10}=\sqrt{7056}*\sqrt{10}=84\sqrt{10}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-84\sqrt{10}}{2*-2520}=\frac{0-84\sqrt{10}}{-5040}
=-\frac{84\sqrt{10}}{-5040}
=-\frac{\sqrt{10}}{-60}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+84\sqrt{10}}{2*-2520}=\frac{0+84\sqrt{10}}{-5040}
=\frac{84\sqrt{10}}{-5040}
=\frac{\sqrt{10}}{-60}
$