42=3x^2-16x+30

Solution for 42=3x^2-16x+30 equation:

42=3x^2-16x+30

We move all terms to the left:

42-(3x^2-16x+30)=0

We get rid of parentheses

-3x^2+16x-30+42=0

We add all the numbers together, and all the variables

-3x^2+16x+12=0

a = -3; b = 16; c = +12;
Δ = b2-4ac
Δ = 162-4·(-3)·12
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-20}{2*-3}=\frac{-36}{-6}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+20}{2*-3}=\frac{4}{-6}
=-2/3
$