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

Solution for (-2z+7)(5z-1)=0 equation:

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

We multiply parentheses ..

(-10z^2+2z+35z-7)=0

We get rid of parentheses

-10z^2+2z+35z-7=0

We add all the numbers together, and all the variables

-10z^2+37z-7=0

a = -10; b = 37; c = -7;
Δ = b2-4ac
Δ = 372-4·(-10)·(-7)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-33}{2*-10}=\frac{-70}{-20}
=3+1/2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+33}{2*-10}=\frac{-4}{-20}
=1/5
$