12x^2+3x=42

Solution for 12x^2+3x=42 equation:

12x^2+3x=42

We move all terms to the left:

12x^2+3x-(42)=0

a = 12; b = 3; c = -42;
Δ = b2-4ac
Δ = 32-4·12·(-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{-(3)-45}{2*12}=\frac{-48}{24}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+45}{2*12}=\frac{42}{24}
=1+3/4
$