3x^2=42-39x

Solution for 3x^2=42-39x equation:

3x^2=42-39x

We move all terms to the left:

3x^2-(42-39x)=0

We add all the numbers together, and all the variables

3x^2-(-39x+42)=0

We get rid of parentheses

3x^2+39x-42=0

a = 3; b = 39; c = -42;
Δ = b2-4ac
Δ = 392-4·3·(-42)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-45}{2*3}=\frac{-84}{6}
=-14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+45}{2*3}=\frac{6}{6}
=1
$