7(b-3)(2b-7)=0

Solution for 7(b-3)(2b-7)=0 equation:

7(b-3)(2b-7)=0

We multiply parentheses ..

7(+2b^2-7b-6b+21)=0

We multiply parentheses

14b^2-49b-42b+147=0

We add all the numbers together, and all the variables

14b^2-91b+147=0

a = 14; b = -91; c = +147;
Δ = b2-4ac
Δ = -912-4·14·147
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-91)-7}{2*14}=\frac{84}{28}
=3
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-91)+7}{2*14}=\frac{98}{28}
=3+1/2
$