(5x+8)(2x-9)=0

Solution for (5x+8)(2x-9)=0 equation:

(5x+8)(2x-9)=0

We multiply parentheses ..

(+10x^2-45x+16x-72)=0

We get rid of parentheses

10x^2-45x+16x-72=0

We add all the numbers together, and all the variables

10x^2-29x-72=0

a = 10; b = -29; c = -72;
Δ = b2-4ac
Δ = -292-4·10·(-72)
Δ = 3721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3721}=61$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-61}{2*10}=\frac{-32}{20}
=-1+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+61}{2*10}=\frac{90}{20}
=4+1/2
$