3x*x-8x-38=0

Solution for 3x*x-8x-38=0 equation:

3x*x-8x-38=0

We add all the numbers together, and all the variables

-8x+3x*x-38=0

Wy multiply elements

3x^2-8x-38=0

a = 3; b = -8; c = -38;
Δ = b2-4ac
Δ = -82-4·3·(-38)
Δ = 520
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:

$\sqrt{\Delta}=\sqrt{520}=\sqrt{4*130}=\sqrt{4}*\sqrt{130}=2\sqrt{130}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{130}}{2*3}=\frac{8-2\sqrt{130}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{130}}{2*3}=\frac{8+2\sqrt{130}}{6}
$