4x^2-14x-143=0

Solution for 4x^2-14x-143=0 equation:

4x^2-14x-143=0

a = 4; b = -14; c = -143;
Δ = b2-4ac
Δ = -142-4·4·(-143)
Δ = 2484
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:

$\sqrt{\Delta}=\sqrt{2484}=\sqrt{36*69}=\sqrt{36}*\sqrt{69}=6\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-6\sqrt{69}}{2*4}=\frac{14-6\sqrt{69}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+6\sqrt{69}}{2*4}=\frac{14+6\sqrt{69}}{8}
$