6x+2=-x(x-23)

Solution for 6x+2=-x(x-23) equation:

6x+2=-x(x-23)

We move all terms to the left:

6x+2-(-x(x-23))=0


We calculate terms in parentheses: -(-x(x-23)), so:

-x(x-23)

We multiply parentheses

-x^2+23x

We add all the numbers together, and all the variables

-1x^2+23x

Back to the equation:

-(-1x^2+23x)


We get rid of parentheses

1x^2-23x+6x+2=0

We add all the numbers together, and all the variables

x^2-17x+2=0

a = 1; b = -17; c = +2;
Δ = b2-4ac
Δ = -172-4·1·2
Δ = 281
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{-(-17)-\sqrt{281}}{2*1}=\frac{17-\sqrt{281}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{281}}{2*1}=\frac{17+\sqrt{281}}{2}
$