24x^2-61x+18=0

Solution for 24x^2-61x+18=0 equation:

24x^2-61x+18=0

a = 24; b = -61; c = +18;
Δ = b2-4ac
Δ = -612-4·24·18
Δ = 1993
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-61)-\sqrt{1993}}{2*24}=\frac{61-\sqrt{1993}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-61)+\sqrt{1993}}{2*24}=\frac{61+\sqrt{1993}}{48}
$