39-(3x+4)=3x(x+7)+x

Solution for 39-(3x+4)=3x(x+7)+x equation:

39-(3x+4)=3x(x+7)+x

We move all terms to the left:

39-(3x+4)-(3x(x+7)+x)=0

We get rid of parentheses

-3x-(3x(x+7)+x)-4+39=0


We calculate terms in parentheses: -(3x(x+7)+x), so:

3x(x+7)+x

We add all the numbers together, and all the variables

x+3x(x+7)

We multiply parentheses

3x^2+x+21x

We add all the numbers together, and all the variables

3x^2+22x

Back to the equation:

-(3x^2+22x)


We add all the numbers together, and all the variables

-3x-(3x^2+22x)+35=0

We get rid of parentheses

-3x^2-3x-22x+35=0

We add all the numbers together, and all the variables

-3x^2-25x+35=0

a = -3; b = -25; c = +35;
Δ = b2-4ac
Δ = -252-4·(-3)·35
Δ = 1045
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{1045}}{2*-3}=\frac{25-\sqrt{1045}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{1045}}{2*-3}=\frac{25+\sqrt{1045}}{-6}
$