1.5x(50-x)=36+x

Solution for 1.5x(50-x)=36+x equation:

1.5x(50-x)=36+x

We move all terms to the left:

1.5x(50-x)-(36+x)=0

We add all the numbers together, and all the variables

1.5x(-1x+50)-(x+36)=0

We multiply parentheses

-1x^2+50x-(x+36)=0

We get rid of parentheses

-1x^2+50x-x-36=0

We add all the numbers together, and all the variables

-1x^2+49x-36=0

a = -1; b = 49; c = -36;
Δ = b2-4ac
Δ = 492-4·(-1)·(-36)
Δ = 2257
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{-(49)-\sqrt{2257}}{2*-1}=\frac{-49-\sqrt{2257}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+\sqrt{2257}}{2*-1}=\frac{-49+\sqrt{2257}}{-2}
$