10z^2-4z-142=0

Solution for 10z^2-4z-142=0 equation:

10z^2-4z-142=0

a = 10; b = -4; c = -142;
Δ = b2-4ac
Δ = -42-4·10·(-142)
Δ = 5696
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5696}=\sqrt{64*89}=\sqrt{64}*\sqrt{89}=8\sqrt{89}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8\sqrt{89}}{2*10}=\frac{4-8\sqrt{89}}{20}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8\sqrt{89}}{2*10}=\frac{4+8\sqrt{89}}{20}
$