3x^2-29x+38=-2

Solution for 3x^2-29x+38=-2 equation:

3x^2-29x+38=-2

We move all terms to the left:

3x^2-29x+38-(-2)=0

We add all the numbers together, and all the variables

3x^2-29x+40=0

a = 3; b = -29; c = +40;
Δ = b2-4ac
Δ = -292-4·3·40
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-19}{2*3}=\frac{10}{6}
=1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+19}{2*3}=\frac{48}{6}
=8
$