4x2+2=38,x=3

Solution for 4x2+2=38,x=3 equation:

4x^2+2=38.x=3

We move all terms to the left:

4x^2+2-(38.x)=0

We add all the numbers together, and all the variables

4x^2-(+38.x)+2=0

We get rid of parentheses

4x^2-38.x+2=0

We add all the numbers together, and all the variables

4x^2-38x+2=0

a = 4; b = -38; c = +2;
Δ = b2-4ac
Δ = -382-4·4·2
Δ = 1412
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:

$\sqrt{\Delta}=\sqrt{1412}=\sqrt{4*353}=\sqrt{4}*\sqrt{353}=2\sqrt{353}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{353}}{2*4}=\frac{38-2\sqrt{353}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{353}}{2*4}=\frac{38+2\sqrt{353}}{8}
$