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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-12x^2-7x+10=0

a = -12; b = -7; c = +10;
Δ = b2-4ac
Δ = -72-4·(-12)·10
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-23}{2*-12}=\frac{-16}{-24}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+23}{2*-12}=\frac{30}{-24}
=-1+1/4
$