-24x2-45x+6=0

Solution for -24x2-45x+6=0 equation:

-24x^2-45x+6=0

a = -24; b = -45; c = +6;
Δ = b2-4ac
Δ = -452-4·(-24)·6
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-51}{2*-24}=\frac{-6}{-48}
=1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+51}{2*-24}=\frac{96}{-48}
=-2
$