4x(3x+2)+5x=6(2x+8)-12

Solution for 4x(3x+2)+5x=6(2x+8)-12 equation:

4x(3x+2)+5x=6(2x+8)-12

We move all terms to the left:

4x(3x+2)+5x-(6(2x+8)-12)=0

We add all the numbers together, and all the variables

5x+4x(3x+2)-(6(2x+8)-12)=0

We multiply parentheses

12x^2+5x+8x-(6(2x+8)-12)=0


We calculate terms in parentheses: -(6(2x+8)-12), so:

6(2x+8)-12

We multiply parentheses

12x+48-12

We add all the numbers together, and all the variables

12x+36

Back to the equation:

-(12x+36)


We add all the numbers together, and all the variables

12x^2+13x-(12x+36)=0

We get rid of parentheses

12x^2+13x-12x-36=0

We add all the numbers together, and all the variables

12x^2+x-36=0

a = 12; b = 1; c = -36;
Δ = b2-4ac
Δ = 12-4·12·(-36)
Δ = 1729
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{-(1)-\sqrt{1729}}{2*12}=\frac{-1-\sqrt{1729}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1729}}{2*12}=\frac{-1+\sqrt{1729}}{24}
$