12x+8-15=-2x(3x-82)

Solution for 12x+8-15=-2x(3x-82) equation:

12x+8-15=-2x(3x-82)

We move all terms to the left:

12x+8-15-(-2x(3x-82))=0

We add all the numbers together, and all the variables

12x-(-2x(3x-82))-7=0


We calculate terms in parentheses: -(-2x(3x-82)), so:

-2x(3x-82)

We multiply parentheses

-6x^2+164x

Back to the equation:

-(-6x^2+164x)


We get rid of parentheses

6x^2-164x+12x-7=0

We add all the numbers together, and all the variables

6x^2-152x-7=0

a = 6; b = -152; c = -7;
Δ = b2-4ac
Δ = -1522-4·6·(-7)
Δ = 23272
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:

$\sqrt{\Delta}=\sqrt{23272}=\sqrt{4*5818}=\sqrt{4}*\sqrt{5818}=2\sqrt{5818}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-152)-2\sqrt{5818}}{2*6}=\frac{152-2\sqrt{5818}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-152)+2\sqrt{5818}}{2*6}=\frac{152+2\sqrt{5818}}{12}
$