(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+61x+72=0

a = 10; b = 61; c = +72;
Δ = b2-4ac
Δ = 612-4·10·72
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(61)-29}{2*10}=\frac{-90}{20}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(61)+29}{2*10}=\frac{-32}{20}
=-1+3/5
$