-5z2-3z-11=-6z2

Solution for -5z2-3z-11=-6z2 equation:

-5z^2-3z-11=-6z^2

We move all terms to the left:

-5z^2-3z-11-(-6z^2)=0

We get rid of parentheses

-5z^2+6z^2-3z-11=0

We add all the numbers together, and all the variables

z^2-3z-11=0

a = 1; b = -3; c = -11;
Δ = b2-4ac
Δ = -32-4·1·(-11)
Δ = 53
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{-(-3)-\sqrt{53}}{2*1}=\frac{3-\sqrt{53}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{53}}{2*1}=\frac{3+\sqrt{53}}{2}
$