2z^2+13z=-3

Solution for 2z^2+13z=-3 equation:

2z^2+13z=-3

We move all terms to the left:

2z^2+13z-(-3)=0

We add all the numbers together, and all the variables

2z^2+13z+3=0

a = 2; b = 13; c = +3;
Δ = b2-4ac
Δ = 132-4·2·3
Δ = 145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-\sqrt{145}}{2*2}=\frac{-13-\sqrt{145}}{4}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{145}}{2*2}=\frac{-13+\sqrt{145}}{4}
$