6b^2+25=409

Solution for 6b^2+25=409 equation:

6b^2+25=409

We move all terms to the left:

6b^2+25-(409)=0

We add all the numbers together, and all the variables

6b^2-384=0

a = 6; b = 0; c = -384;
Δ = b2-4ac
Δ = 02-4·6·(-384)
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-96}{2*6}=\frac{-96}{12}
=-8
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+96}{2*6}=\frac{96}{12}
=8
$