(5x+9)(12x-17)=0

Solution for (5x+9)(12x-17)=0 equation:

(5x+9)(12x-17)=0

We multiply parentheses ..

(+60x^2-85x+108x-153)=0

We get rid of parentheses

60x^2-85x+108x-153=0

We add all the numbers together, and all the variables

60x^2+23x-153=0

a = 60; b = 23; c = -153;
Δ = b2-4ac
Δ = 232-4·60·(-153)
Δ = 37249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{37249}=193$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-193}{2*60}=\frac{-216}{120}
=-1+4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+193}{2*60}=\frac{170}{120}
=1+5/12
$