24x^2-45x+21=0

Solution for 24x^2-45x+21=0 equation:

24x^2-45x+21=0

a = 24; b = -45; c = +21;
Δ = b2-4ac
Δ = -452-4·24·21
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-3}{2*24}=\frac{42}{48}
=7/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+3}{2*24}=\frac{48}{48}
=1
$