-12a^2-10a+42=0

Solution for -12a^2-10a+42=0 equation:

-12a^2-10a+42=0

a = -12; b = -10; c = +42;
Δ = b2-4ac
Δ = -102-4·(-12)·42
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-46}{2*-12}=\frac{-36}{-24}
=1+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+46}{2*-12}=\frac{56}{-24}
=-2+1/3
$