(100-2x)(3x+50)=58,682

Solution for (100-2x)(3x+50)=58,682 equation:

(100-2x)(3x+50)=58.682

We move all terms to the left:

(100-2x)(3x+50)-(58.682)=0

We add all the numbers together, and all the variables

(-2x+100)(3x+50)-(58.682)=0

We add all the numbers together, and all the variables

(-2x+100)(3x+50)-58.682=0

We multiply parentheses ..

(-6x^2-100x+300x+5000)-58.682=0

We get rid of parentheses

-6x^2-100x+300x+5000-58.682=0

We add all the numbers together, and all the variables

-6x^2+200x+4941.318=0

a = -6; b = 200; c = +4941.318;
Δ = b2-4ac
Δ = 2002-4·(-6)·4941.318
Δ = 158591.632
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-\sqrt{158591.632}}{2*-6}=\frac{-200-\sqrt{158591.632}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+\sqrt{158591.632}}{2*-6}=\frac{-200+\sqrt{158591.632}}{-12}
$