5(3+x)=x(x-3)-4x

Solution for 5(3+x)=x(x-3)-4x equation:

5(3+x)=x(x-3)-4x

We move all terms to the left:

5(3+x)-(x(x-3)-4x)=0

We add all the numbers together, and all the variables

5(x+3)-(x(x-3)-4x)=0

We multiply parentheses

5x-(x(x-3)-4x)+15=0


We calculate terms in parentheses: -(x(x-3)-4x), so:

x(x-3)-4x

We add all the numbers together, and all the variables

-4x+x(x-3)

We multiply parentheses

x^2-4x-3x

We add all the numbers together, and all the variables

x^2-7x

Back to the equation:

-(x^2-7x)


We get rid of parentheses

-x^2+5x+7x+15=0

We add all the numbers together, and all the variables

-1x^2+12x+15=0

a = -1; b = 12; c = +15;
Δ = b2-4ac
Δ = 122-4·(-1)·15
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{51}}{2*-1}=\frac{-12-2\sqrt{51}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{51}}{2*-1}=\frac{-12+2\sqrt{51}}{-2}
$