23x^2-14x-3=0

Solution for 23x^2-14x-3=0 equation:

23x^2-14x-3=0

a = 23; b = -14; c = -3;
Δ = b2-4ac
Δ = -142-4·23·(-3)
Δ = 472
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:

$\sqrt{\Delta}=\sqrt{472}=\sqrt{4*118}=\sqrt{4}*\sqrt{118}=2\sqrt{118}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{118}}{2*23}=\frac{14-2\sqrt{118}}{46}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{118}}{2*23}=\frac{14+2\sqrt{118}}{46}
$