6x(4+2x)=2x-(7x-4)+5

Solution for 6x(4+2x)=2x-(7x-4)+5 equation:

6x(4+2x)=2x-(7x-4)+5

We move all terms to the left:

6x(4+2x)-(2x-(7x-4)+5)=0

We add all the numbers together, and all the variables

6x(2x+4)-(2x-(7x-4)+5)=0

We multiply parentheses

12x^2+24x-(2x-(7x-4)+5)=0


We calculate terms in parentheses: -(2x-(7x-4)+5), so:

2x-(7x-4)+5

We get rid of parentheses

2x-7x+4+5

We add all the numbers together, and all the variables

-5x+9

Back to the equation:

-(-5x+9)


We get rid of parentheses

12x^2+24x+5x-9=0

We add all the numbers together, and all the variables

12x^2+29x-9=0

a = 12; b = 29; c = -9;
Δ = b2-4ac
Δ = 292-4·12·(-9)
Δ = 1273
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{-(29)-\sqrt{1273}}{2*12}=\frac{-29-\sqrt{1273}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+\sqrt{1273}}{2*12}=\frac{-29+\sqrt{1273}}{24}
$