34+x=3x(12+x)-24

Solution for 34+x=3x(12+x)-24 equation:

34+x=3x(12+x)-24

We move all terms to the left:

34+x-(3x(12+x)-24)=0

We add all the numbers together, and all the variables

x-(3x(x+12)-24)+34=0


We calculate terms in parentheses: -(3x(x+12)-24), so:

3x(x+12)-24

We multiply parentheses

3x^2+36x-24

Back to the equation:

-(3x^2+36x-24)


We get rid of parentheses

-3x^2+x-36x+24+34=0

We add all the numbers together, and all the variables

-3x^2-35x+58=0

a = -3; b = -35; c = +58;
Δ = b2-4ac
Δ = -352-4·(-3)·58
Δ = 1921
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{-(-35)-\sqrt{1921}}{2*-3}=\frac{35-\sqrt{1921}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{1921}}{2*-3}=\frac{35+\sqrt{1921}}{-6}
$