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

Solution for z=(5z+7)(2-z)=0 equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

z-((5z+7)(-1z+2))=0

We multiply parentheses ..

-((-5z^2+10z-7z+14))+z=0


We calculate terms in parentheses: -((-5z^2+10z-7z+14)), so:

(-5z^2+10z-7z+14)

We get rid of parentheses

-5z^2+10z-7z+14

We add all the numbers together, and all the variables

-5z^2+3z+14

Back to the equation:

-(-5z^2+3z+14)


We get rid of parentheses

5z^2-3z+z-14=0

We add all the numbers together, and all the variables

5z^2-2z-14=0

a = 5; b = -2; c = -14;
Δ = b2-4ac
Δ = -22-4·5·(-14)
Δ = 284
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:

$\sqrt{\Delta}=\sqrt{284}=\sqrt{4*71}=\sqrt{4}*\sqrt{71}=2\sqrt{71}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{71}}{2*5}=\frac{2-2\sqrt{71}}{10}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{71}}{2*5}=\frac{2+2\sqrt{71}}{10}
$