5b2-4=42

Solution for 5b2-4=42 equation:

5b^2-4=42

We move all terms to the left:

5b^2-4-(42)=0

We add all the numbers together, and all the variables

5b^2-46=0

a = 5; b = 0; c = -46;
Δ = b2-4ac
Δ = 02-4·5·(-46)
Δ = 920
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:

$\sqrt{\Delta}=\sqrt{920}=\sqrt{4*230}=\sqrt{4}*\sqrt{230}=2\sqrt{230}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{230}}{2*5}=\frac{0-2\sqrt{230}}{10}
=-\frac{2\sqrt{230}}{10}
=-\frac{\sqrt{230}}{5}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{230}}{2*5}=\frac{0+2\sqrt{230}}{10}
=\frac{2\sqrt{230}}{10}
=\frac{\sqrt{230}}{5}
$