2z^2-7z=-3

Solution for 2z^2-7z=-3 equation:

2z^2-7z=-3

We move all terms to the left:

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

We add all the numbers together, and all the variables

2z^2-7z+3=0

a = 2; b = -7; c = +3;
Δ = b2-4ac
Δ = -72-4·2·3
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-5}{2*2}=\frac{2}{4}
=1/2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+5}{2*2}=\frac{12}{4}
=3
$