5b^2+2b^2=96

Solution for 5b^2+2b^2=96 equation:

5b^2+2b^2=96

We move all terms to the left:

5b^2+2b^2-(96)=0

We add all the numbers together, and all the variables

7b^2-96=0

a = 7; b = 0; c = -96;
Δ = b2-4ac
Δ = 02-4·7·(-96)
Δ = 2688
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:

$\sqrt{\Delta}=\sqrt{2688}=\sqrt{64*42}=\sqrt{64}*\sqrt{42}=8\sqrt{42}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{42}}{2*7}=\frac{0-8\sqrt{42}}{14}
=-\frac{8\sqrt{42}}{14}
=-\frac{4\sqrt{42}}{7}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{42}}{2*7}=\frac{0+8\sqrt{42}}{14}
=\frac{8\sqrt{42}}{14}
=\frac{4\sqrt{42}}{7}
$