(3x+5)(-1/2x+16)=0

Solution for (3x+5)(-1/2x+16)=0 equation:

(3x+5)(-1/2x+16)=0


Domain of the equation: 2x+16)!=0

x∈R


We multiply parentheses ..

(-3x^2+48x-5x+80)=0

We get rid of parentheses

-3x^2+48x-5x+80=0

We add all the numbers together, and all the variables

-3x^2+43x+80=0

a = -3; b = 43; c = +80;
Δ = b2-4ac
Δ = 432-4·(-3)·80
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-53}{2*-3}=\frac{-96}{-6}
=+16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+53}{2*-3}=\frac{10}{-6}
=-1+2/3
$