-24x^2+67x-45=0

Solution for -24x^2+67x-45=0 equation:

-24x^2+67x-45=0

a = -24; b = 67; c = -45;
Δ = b2-4ac
Δ = 672-4·(-24)·(-45)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(67)-13}{2*-24}=\frac{-80}{-48}
=1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(67)+13}{2*-24}=\frac{-54}{-48}
=1+1/8
$