6b^2=b^2+7-b

Solution for 6b^2=b^2+7-b equation:

6b^2=b^2+7-b

We move all terms to the left:

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

We get rid of parentheses

6b^2-b^2+b-7=0

We add all the numbers together, and all the variables

5b^2+b-7=0

a = 5; b = 1; c = -7;
Δ = b2-4ac
Δ = 12-4·5·(-7)
Δ = 141
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{141}}{2*5}=\frac{-1-\sqrt{141}}{10}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{141}}{2*5}=\frac{-1+\sqrt{141}}{10}
$