24x^2-4x=140

Solution for 24x^2-4x=140 equation:

24x^2-4x=140

We move all terms to the left:

24x^2-4x-(140)=0

a = 24; b = -4; c = -140;
Δ = b2-4ac
Δ = -42-4·24·(-140)
Δ = 13456
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13456}=116$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-116}{2*24}=\frac{-112}{48}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+116}{2*24}=\frac{120}{48}
=2+1/2
$