(5x+6)(x-4)=0

Solution for (5x+6)(x-4)=0 equation:

(5x+6)(x-4)=0

We multiply parentheses ..

(+5x^2-20x+6x-24)=0

We get rid of parentheses

5x^2-20x+6x-24=0

We add all the numbers together, and all the variables

5x^2-14x-24=0

a = 5; b = -14; c = -24;
Δ = b2-4ac
Δ = -142-4·5·(-24)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-26}{2*5}=\frac{-12}{10}
=-1+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+26}{2*5}=\frac{40}{10}
=4
$