(5x+4)(2x+5)=0

Solution for (5x+4)(2x+5)=0 equation:

(5x+4)(2x+5)=0

We multiply parentheses ..

(+10x^2+25x+8x+20)=0

We get rid of parentheses

10x^2+25x+8x+20=0

We add all the numbers together, and all the variables

10x^2+33x+20=0

a = 10; b = 33; c = +20;
Δ = b2-4ac
Δ = 332-4·10·20
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-17}{2*10}=\frac{-50}{20}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+17}{2*10}=\frac{-16}{20}
=-4/5
$