24x^2-46x+10=0

Solution for 24x^2-46x+10=0 equation:

24x^2-46x+10=0

a = 24; b = -46; c = +10;
Δ = b2-4ac
Δ = -462-4·24·10
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-34}{2*24}=\frac{12}{48}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+34}{2*24}=\frac{80}{48}
=1+2/3
$