2(7x)^2-2(7x)-24=0

Solution for 2(7x)^2-2(7x)-24=0 equation:

2(7x)^2-2(7x)-24=0

a = 27; b = -27; c = -24;
Δ = b2-4ac
Δ = -272-4·27·(-24)
Δ = 3321
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3321}=\sqrt{81*41}=\sqrt{81}*\sqrt{41}=9\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-9\sqrt{41}}{2*27}=\frac{27-9\sqrt{41}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+9\sqrt{41}}{2*27}=\frac{27+9\sqrt{41}}{54}
$