5b^2+4b^2=360

Solution for 5b^2+4b^2=360 equation:

5b^2+4b^2=360

We move all terms to the left:

5b^2+4b^2-(360)=0

We add all the numbers together, and all the variables

9b^2-360=0

a = 9; b = 0; c = -360;
Δ = b2-4ac
Δ = 02-4·9·(-360)
Δ = 12960
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:

$\sqrt{\Delta}=\sqrt{12960}=\sqrt{1296*10}=\sqrt{1296}*\sqrt{10}=36\sqrt{10}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{10}}{2*9}=\frac{0-36\sqrt{10}}{18}
=-\frac{36\sqrt{10}}{18}
=-2\sqrt{10}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{10}}{2*9}=\frac{0+36\sqrt{10}}{18}
=\frac{36\sqrt{10}}{18}
=2\sqrt{10}
$