30b^2-78=-36

Solution for 30b^2-78=-36 equation:

30b^2-78=-36

We move all terms to the left:

30b^2-78-(-36)=0

We add all the numbers together, and all the variables

30b^2-42=0

a = 30; b = 0; c = -42;
Δ = b2-4ac
Δ = 02-4·30·(-42)
Δ = 5040
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:

$\sqrt{\Delta}=\sqrt{5040}=\sqrt{144*35}=\sqrt{144}*\sqrt{35}=12\sqrt{35}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{35}}{2*30}=\frac{0-12\sqrt{35}}{60}
=-\frac{12\sqrt{35}}{60}
=-\frac{\sqrt{35}}{5}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{35}}{2*30}=\frac{0+12\sqrt{35}}{60}
=\frac{12\sqrt{35}}{60}
=\frac{\sqrt{35}}{5}
$