(2z+5)(5z-6)=90

Solution for (2z+5)(5z-6)=90 equation:

(2z+5)(5z-6)=90

We move all terms to the left:

(2z+5)(5z-6)-(90)=0

We multiply parentheses ..

(+10z^2-12z+25z-30)-90=0

We get rid of parentheses

10z^2-12z+25z-30-90=0

We add all the numbers together, and all the variables

10z^2+13z-120=0

a = 10; b = 13; c = -120;
Δ = b2-4ac
Δ = 132-4·10·(-120)
Δ = 4969
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{-(13)-\sqrt{4969}}{2*10}=\frac{-13-\sqrt{4969}}{20}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{4969}}{2*10}=\frac{-13+\sqrt{4969}}{20}
$