6z=5(-2z-7)z=1

Solution for 6z=5(-2z-7)z=1 equation:

6z=5(-2z-7)z=1

We move all terms to the left:

6z-(5(-2z-7)z)=0


We calculate terms in parentheses: -(5(-2z-7)z), so:

5(-2z-7)z

We multiply parentheses

-10z^2-35z

Back to the equation:

-(-10z^2-35z)


We get rid of parentheses

10z^2+35z+6z=0

We add all the numbers together, and all the variables

10z^2+41z=0

a = 10; b = 41; c = 0;
Δ = b2-4ac
Δ = 412-4·10·0
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-41}{2*10}=\frac{-82}{20}
=-4+1/10
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+41}{2*10}=\frac{0}{20}
=0
$