13z+6=5z^2

Solution for 13z+6=5z^2 equation:

13z+6=5z^2

We move all terms to the left:

13z+6-(5z^2)=0

determiningTheFunctionDomain
-5z^2+13z+6=0

a = -5; b = 13; c = +6;
Δ = b2-4ac
Δ = 132-4·(-5)·6
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-17}{2*-5}=\frac{-30}{-10}
=+3
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+17}{2*-5}=\frac{4}{-10}
=-2/5
$