3x2+3=24x-42

Solution for 3x2+3=24x-42 equation:

3x^2+3=24x-42

We move all terms to the left:

3x^2+3-(24x-42)=0

We get rid of parentheses

3x^2-24x+42+3=0

We add all the numbers together, and all the variables

3x^2-24x+45=0

a = 3; b = -24; c = +45;
Δ = b2-4ac
Δ = -242-4·3·45
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-6}{2*3}=\frac{18}{6}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+6}{2*3}=\frac{30}{6}
=5
$