3x^2-9x=38

Solution for 3x^2-9x=38 equation:

3x^2-9x=38

We move all terms to the left:

3x^2-9x-(38)=0

a = 3; b = -9; c = -38;
Δ = b2-4ac
Δ = -92-4·3·(-38)
Δ = 537
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{-(-9)-\sqrt{537}}{2*3}=\frac{9-\sqrt{537}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{537}}{2*3}=\frac{9+\sqrt{537}}{6}
$