(4x-10)(24-5x)=0

Solution for (4x-10)(24-5x)=0 equation:

(4x-10)(24-5x)=0

We add all the numbers together, and all the variables

(4x-10)(-5x+24)=0

We multiply parentheses ..

(-20x^2+96x+50x-240)=0

We get rid of parentheses

-20x^2+96x+50x-240=0

We add all the numbers together, and all the variables

-20x^2+146x-240=0

a = -20; b = 146; c = -240;
Δ = b2-4ac
Δ = 1462-4·(-20)·(-240)
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(146)-46}{2*-20}=\frac{-192}{-40}
=4+4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(146)+46}{2*-20}=\frac{-100}{-40}
=2+1/2
$