53x2-2x-7=0

Solution for 53x2-2x-7=0 equation:

53x^2-2x-7=0

a = 53; b = -2; c = -7;
Δ = b2-4ac
Δ = -22-4·53·(-7)
Δ = 1488
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:

$\sqrt{\Delta}=\sqrt{1488}=\sqrt{16*93}=\sqrt{16}*\sqrt{93}=4\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{93}}{2*53}=\frac{2-4\sqrt{93}}{106}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{93}}{2*53}=\frac{2+4\sqrt{93}}{106}
$