38x(x-4)+4=0

Solution for 38x(x-4)+4=0 equation:

38x(x-4)+4=0

We multiply parentheses

38x^2-152x+4=0

a = 38; b = -152; c = +4;
Δ = b2-4ac
Δ = -1522-4·38·4
Δ = 22496
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:

$\sqrt{\Delta}=\sqrt{22496}=\sqrt{16*1406}=\sqrt{16}*\sqrt{1406}=4\sqrt{1406}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-152)-4\sqrt{1406}}{2*38}=\frac{152-4\sqrt{1406}}{76}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-152)+4\sqrt{1406}}{2*38}=\frac{152+4\sqrt{1406}}{76}
$