12x^2-3x-42=0

Solution for 12x^2-3x-42=0 equation:

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{-42}{24}
=-1+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+45}{2*12}=\frac{48}{24}
=2
$