24x^2+140x-196=0

Solution for 24x^2+140x-196=0 equation:

24x^2+140x-196=0

a = 24; b = 140; c = -196;
Δ = b2-4ac
Δ = 1402-4·24·(-196)
Δ = 38416
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{38416}=196$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(140)-196}{2*24}=\frac{-336}{48}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(140)+196}{2*24}=\frac{56}{48}
=1+1/6
$