5x^2+2=4x^2+47

Solution for 5x^2+2=4x^2+47 equation:

5x^2+2=4x^2+47

We move all terms to the left:

5x^2+2-(4x^2+47)=0

We get rid of parentheses

5x^2-4x^2-47+2=0

We add all the numbers together, and all the variables

x^2-45=0

a = 1; b = 0; c = -45;
Δ = b2-4ac
Δ = 02-4·1·(-45)
Δ = 180
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{5}}{2*1}=\frac{0-6\sqrt{5}}{2}
=-\frac{6\sqrt{5}}{2}
=-3\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{5}}{2*1}=\frac{0+6\sqrt{5}}{2}
=\frac{6\sqrt{5}}{2}
=3\sqrt{5}
$