5x-x(x-18)=6-2(x+15)

Solution for 5x-x(x-18)=6-2(x+15) equation:

5x-x(x-18)=6-2(x+15)

We move all terms to the left:

5x-x(x-18)-(6-2(x+15))=0

We multiply parentheses

-x^2+5x+18x-(6-2(x+15))=0


We calculate terms in parentheses: -(6-2(x+15)), so:

6-2(x+15)

determiningTheFunctionDomain
-2(x+15)+6

We multiply parentheses

-2x-30+6

We add all the numbers together, and all the variables

-2x-24

Back to the equation:

-(-2x-24)


We add all the numbers together, and all the variables

-1x^2+23x-(-2x-24)=0

We get rid of parentheses

-1x^2+23x+2x+24=0

We add all the numbers together, and all the variables

-1x^2+25x+24=0

a = -1; b = 25; c = +24;
Δ = b2-4ac
Δ = 252-4·(-1)·24
Δ = 721
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{-(25)-\sqrt{721}}{2*-1}=\frac{-25-\sqrt{721}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{721}}{2*-1}=\frac{-25+\sqrt{721}}{-2}
$