6992=x(260-2x)

Solution for 6992=x(260-2x) equation:

6992=x(260-2x)

We move all terms to the left:

6992-(x(260-2x))=0

We add all the numbers together, and all the variables

-(x(-2x+260))+6992=0


We calculate terms in parentheses: -(x(-2x+260)), so:

x(-2x+260)

We multiply parentheses

-2x^2+260x

Back to the equation:

-(-2x^2+260x)


We get rid of parentheses

2x^2-260x+6992=0

a = 2; b = -260; c = +6992;
Δ = b2-4ac
Δ = -2602-4·2·6992
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-260)-108}{2*2}=\frac{152}{4}
=38
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-260)+108}{2*2}=\frac{368}{4}
=92
$