4z*5z-3=174

Solution for 4z*5z-3=174 equation:

4z*5z-3=174

We move all terms to the left:

4z*5z-3-(174)=0

We add all the numbers together, and all the variables

4z*5z-177=0

Wy multiply elements

20z^2-177=0

a = 20; b = 0; c = -177;
Δ = b2-4ac
Δ = 02-4·20·(-177)
Δ = 14160
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:

$\sqrt{\Delta}=\sqrt{14160}=\sqrt{16*885}=\sqrt{16}*\sqrt{885}=4\sqrt{885}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{885}}{2*20}=\frac{0-4\sqrt{885}}{40}
=-\frac{4\sqrt{885}}{40}
=-\frac{\sqrt{885}}{10}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{885}}{2*20}=\frac{0+4\sqrt{885}}{40}
=\frac{4\sqrt{885}}{40}
=\frac{\sqrt{885}}{10}
$