5.8+3.5z(z-4)=3.5(z+2)

Solution for 5.8+3.5z(z-4)=3.5(z+2) equation:

5.8+3.5z(z-4)=3.5(z+2)

We move all terms to the left:

5.8+3.5z(z-4)-(3.5(z+2))=0

We multiply parentheses

3z^2-12z-(3.5(z+2))+5.8=0


We calculate terms in parentheses: -(3.5(z+2)), so:

3.5(z+2)

We multiply parentheses

3.5z+7

Back to the equation:

-(3.5z+7)


We get rid of parentheses

3z^2-12z-3.5z-7+5.8=0

We add all the numbers together, and all the variables

3z^2-15.5z-1.2=0

a = 3; b = -15.5; c = -1.2;
Δ = b2-4ac
Δ = -15.52-4·3·(-1.2)
Δ = 254.65
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{-(-15.5)-\sqrt{254.65}}{2*3}=\frac{15.5-\sqrt{254.65}}{6}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15.5)+\sqrt{254.65}}{2*3}=\frac{15.5+\sqrt{254.65}}{6}
$