(x+5)+((37-x)+8)=x(37-x)+300

Solution for (x+5)+((37-x)+8)=x(37-x)+300 equation:

(x+5)+((37-x)+8)=x(37-x)+300

We move all terms to the left:

(x+5)+((37-x)+8)-(x(37-x)+300)=0

We add all the numbers together, and all the variables

(x+5)+((-1x+37)+8)-(x(-1x+37)+300)=0

We get rid of parentheses

x+((-1x+37)+8)-(x(-1x+37)+300)+5=0


We calculate terms in parentheses: +((-1x+37)+8), so:

(-1x+37)+8

We get rid of parentheses

-1x+37+8

We add all the numbers together, and all the variables

-1x+45

Back to the equation:

+(-1x+45)



We calculate terms in parentheses: -(x(-1x+37)+300), so:

x(-1x+37)+300

We multiply parentheses

-1x^2+37x+300

Back to the equation:

-(-1x^2+37x+300)


We get rid of parentheses

1x^2-37x+x-1x-300+45+5=0

We add all the numbers together, and all the variables

x^2-37x-250=0

a = 1; b = -37; c = -250;
Δ = b2-4ac
Δ = -372-4·1·(-250)
Δ = 2369
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{-(-37)-\sqrt{2369}}{2*1}=\frac{37-\sqrt{2369}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+\sqrt{2369}}{2*1}=\frac{37+\sqrt{2369}}{2}
$