(5x+4)(-2x-3)=0

Solution for (5x+4)(-2x-3)=0 equation:

(5x+4)(-2x-3)=0

We multiply parentheses ..

(-10x^2-15x-8x-12)=0

We get rid of parentheses

-10x^2-15x-8x-12=0

We add all the numbers together, and all the variables

-10x^2-23x-12=0

a = -10; b = -23; c = -12;
Δ = b2-4ac
Δ = -232-4·(-10)·(-12)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-7}{2*-10}=\frac{16}{-20}
=-4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+7}{2*-10}=\frac{30}{-20}
=-1+1/2
$