2/3*b=70

Solution for 2/3*b=70 equation:

2/3*b=70

We move all terms to the left:

2/3*b-(70)=0


Domain of the equation: 3*b!=0

b!=0/1

b!=0

b∈R


We multiply all the terms by the denominator


-70*3*b+2=0

Wy multiply elements

-210b*b+2=0

Wy multiply elements

-210b^2+2=0

a = -210; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-210)·2
Δ = 1680
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:

$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{105}}{2*-210}=\frac{0-4\sqrt{105}}{-420}
=-\frac{4\sqrt{105}}{-420}
=-\frac{\sqrt{105}}{-105}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{105}}{2*-210}=\frac{0+4\sqrt{105}}{-420}
=\frac{4\sqrt{105}}{-420}
=\frac{\sqrt{105}}{-105}
$