7b^2-1=223

Solution for 7b^2-1=223 equation:

7b^2-1=223

We move all terms to the left:

7b^2-1-(223)=0

We add all the numbers together, and all the variables

7b^2-224=0

a = 7; b = 0; c = -224;
Δ = b2-4ac
Δ = 02-4·7·(-224)
Δ = 6272
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:

$\sqrt{\Delta}=\sqrt{6272}=\sqrt{3136*2}=\sqrt{3136}*\sqrt{2}=56\sqrt{2}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-56\sqrt{2}}{2*7}=\frac{0-56\sqrt{2}}{14}
=-\frac{56\sqrt{2}}{14}
=-4\sqrt{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+56\sqrt{2}}{2*7}=\frac{0+56\sqrt{2}}{14}
=\frac{56\sqrt{2}}{14}
=4\sqrt{2}
$