2(0.5z+7)=z(z-5)

Solution for 2(0.5z+7)=z(z-5) equation:

2(0.5z+7)=z(z-5)

We move all terms to the left:

2(0.5z+7)-(z(z-5))=0

We multiply parentheses

0z-(z(z-5))+14=0


We calculate terms in parentheses: -(z(z-5)), so:

z(z-5)

We multiply parentheses

z^2-5z

Back to the equation:

-(z^2-5z)


We add all the numbers together, and all the variables

z-(z^2-5z)+14=0

We get rid of parentheses

-z^2+z+5z+14=0

We add all the numbers together, and all the variables

-1z^2+6z+14=0

a = -1; b = 6; c = +14;
Δ = b2-4ac
Δ = 62-4·(-1)·14
Δ = 92
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{23}}{2*-1}=\frac{-6-2\sqrt{23}}{-2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{23}}{2*-1}=\frac{-6+2\sqrt{23}}{-2}
$