-4a^2-5a+6=0

Solution for -4a^2-5a+6=0 equation:

-4a^2-5a+6=0

a = -4; b = -5; c = +6;
Δ = b2-4ac
Δ = -52-4·(-4)·6
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-11}{2*-4}=\frac{-6}{-8}
=3/4
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+11}{2*-4}=\frac{16}{-8}
=-2
$