570=2x(37+60-2x)

Solution for 570=2x(37+60-2x) equation:

570=2x(37+60-2x)

We move all terms to the left:

570-(2x(37+60-2x))=0

We add all the numbers together, and all the variables

-(2x(-2x+97))+570=0


We calculate terms in parentheses: -(2x(-2x+97)), so:

2x(-2x+97)

We multiply parentheses

-4x^2+194x

Back to the equation:

-(-4x^2+194x)


We get rid of parentheses

4x^2-194x+570=0

a = 4; b = -194; c = +570;
Δ = b2-4ac
Δ = -1942-4·4·570
Δ = 28516
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:

$\sqrt{\Delta}=\sqrt{28516}=\sqrt{4*7129}=\sqrt{4}*\sqrt{7129}=2\sqrt{7129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-194)-2\sqrt{7129}}{2*4}=\frac{194-2\sqrt{7129}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-194)+2\sqrt{7129}}{2*4}=\frac{194+2\sqrt{7129}}{8}
$