2=x(20x-10)

Solution for 2=x(20x-10) equation:

2=x(20x-10)

We move all terms to the left:

2-(x(20x-10))=0


We calculate terms in parentheses: -(x(20x-10)), so:

x(20x-10)

We multiply parentheses

20x^2-10x

Back to the equation:

-(20x^2-10x)


We get rid of parentheses

-20x^2+10x+2=0

a = -20; b = 10; c = +2;
Δ = b2-4ac
Δ = 102-4·(-20)·2
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{65}}{2*-20}=\frac{-10-2\sqrt{65}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{65}}{2*-20}=\frac{-10+2\sqrt{65}}{-40}
$