(60-5x)(32+2x)=1,800

Solution for (60-5x)(32+2x)=1,800 equation:

(60-5x)(32+2x)=1.800

We move all terms to the left:

(60-5x)(32+2x)-(1.800)=0

We add all the numbers together, and all the variables

(-5x+60)(2x+32)-(1.8)=0

We add all the numbers together, and all the variables

(-5x+60)(2x+32)-1.8=0

We multiply parentheses ..

(-10x^2-160x+120x+1920)-1.8=0

We get rid of parentheses

-10x^2-160x+120x+1920-1.8=0

We add all the numbers together, and all the variables

-10x^2-40x+1918.2=0

a = -10; b = -40; c = +1918.2;
Δ = b2-4ac
Δ = -402-4·(-10)·1918.2
Δ = 78328
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{78328}=\sqrt{4*19582}=\sqrt{4}*\sqrt{19582}=2\sqrt{19582}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{19582}}{2*-10}=\frac{40-2\sqrt{19582}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{19582}}{2*-10}=\frac{40+2\sqrt{19582}}{-20}
$