(4x+5)(-3x+8)=0

Solution for (4x+5)(-3x+8)=0 equation:

(4x+5)(-3x+8)=0

We multiply parentheses ..

(-12x^2+32x-15x+40)=0

We get rid of parentheses

-12x^2+32x-15x+40=0

We add all the numbers together, and all the variables

-12x^2+17x+40=0

a = -12; b = 17; c = +40;
Δ = b2-4ac
Δ = 172-4·(-12)·40
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-47}{2*-12}=\frac{-64}{-24}
=2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+47}{2*-12}=\frac{30}{-24}
=-1+1/4
$