7b^2+9=289

Solution for 7b^2+9=289 equation:

7b^2+9=289

We move all terms to the left:

7b^2+9-(289)=0

We add all the numbers together, and all the variables

7b^2-280=0

a = 7; b = 0; c = -280;
Δ = b2-4ac
Δ = 02-4·7·(-280)
Δ = 7840
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:

$\sqrt{\Delta}=\sqrt{7840}=\sqrt{784*10}=\sqrt{784}*\sqrt{10}=28\sqrt{10}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28\sqrt{10}}{2*7}=\frac{0-28\sqrt{10}}{14}
=-\frac{28\sqrt{10}}{14}
=-2\sqrt{10}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28\sqrt{10}}{2*7}=\frac{0+28\sqrt{10}}{14}
=\frac{28\sqrt{10}}{14}
=2\sqrt{10}
$