(53x^2-14x-3)=0

Solution for (53x^2-14x-3)=0 equation:

(53x^2-14x-3)=0

We get rid of parentheses

53x^2-14x-3=0

a = 53; b = -14; c = -3;
Δ = b2-4ac
Δ = -142-4·53·(-3)
Δ = 832
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:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-8\sqrt{13}}{2*53}=\frac{14-8\sqrt{13}}{106}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+8\sqrt{13}}{2*53}=\frac{14+8\sqrt{13}}{106}
$