x(3x-5)=38

Solution for x(3x-5)=38 equation:

x(3x-5)=38

We move all terms to the left:

x(3x-5)-(38)=0

We multiply parentheses

3x^2-5x-38=0

a = 3; b = -5; c = -38;
Δ = b2-4ac
Δ = -52-4·3·(-38)
Δ = 481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{481}}{2*3}=\frac{5-\sqrt{481}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{481}}{2*3}=\frac{5+\sqrt{481}}{6}
$