(5x+1)(8-3x)=0

Solution for (5x+1)(8-3x)=0 equation:

(5x+1)(8-3x)=0

We add all the numbers together, and all the variables

(5x+1)(-3x+8)=0

We multiply parentheses ..

(-15x^2+40x-3x+8)=0

We get rid of parentheses

-15x^2+40x-3x+8=0

We add all the numbers together, and all the variables

-15x^2+37x+8=0

a = -15; b = 37; c = +8;
Δ = b2-4ac
Δ = 372-4·(-15)·8
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-43}{2*-15}=\frac{-80}{-30}
=2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+43}{2*-15}=\frac{6}{-30}
=-1/5
$