2-x(x+9)=(3x+1)(5-x)

Solution for 2-x(x+9)=(3x+1)(5-x) equation:

2-x(x+9)=(3x+1)(5-x)

We move all terms to the left:

2-x(x+9)-((3x+1)(5-x))=0

We add all the numbers together, and all the variables

-x(x+9)-((3x+1)(-1x+5))+2=0

We multiply parentheses

-x^2-9x-((3x+1)(-1x+5))+2=0

We multiply parentheses ..

-x^2-((-3x^2+15x-1x+5))-9x+2=0


We calculate terms in parentheses: -((-3x^2+15x-1x+5)), so:

(-3x^2+15x-1x+5)

We get rid of parentheses

-3x^2+15x-1x+5

We add all the numbers together, and all the variables

-3x^2+14x+5

Back to the equation:

-(-3x^2+14x+5)


We add all the numbers together, and all the variables

-1x^2-(-3x^2+14x+5)-9x+2=0

We get rid of parentheses

-1x^2+3x^2-14x-9x-5+2=0

We add all the numbers together, and all the variables

2x^2-23x-3=0

a = 2; b = -23; c = -3;
Δ = b2-4ac
Δ = -232-4·2·(-3)
Δ = 553
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{-(-23)-\sqrt{553}}{2*2}=\frac{23-\sqrt{553}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{553}}{2*2}=\frac{23+\sqrt{553}}{4}
$