7z^2+8z+3=3z^2

Solution for 7z^2+8z+3=3z^2 equation:

7z^2+8z+3=3z^2

We move all terms to the left:

7z^2+8z+3-(3z^2)=0

determiningTheFunctionDomain
7z^2-3z^2+8z+3=0

We add all the numbers together, and all the variables

4z^2+8z+3=0

a = 4; b = 8; c = +3;
Δ = b2-4ac
Δ = 82-4·4·3
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4}{2*4}=\frac{-12}{8}
=-1+1/2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4}{2*4}=\frac{-4}{8}
=-1/2
$