2x+7-5x+8=3(5+6x)12x

Solution for 2x+7-5x+8=3(5+6x)12x equation:

2x+7-5x+8=3(5+6x)12x

We move all terms to the left:

2x+7-5x+8-(3(5+6x)12x)=0

We add all the numbers together, and all the variables

2x-5x-(3(6x+5)12x)+7+8=0

We add all the numbers together, and all the variables

-3x-(3(6x+5)12x)+15=0


We calculate terms in parentheses: -(3(6x+5)12x), so:

3(6x+5)12x

We multiply parentheses

216x^2+180x

Back to the equation:

-(216x^2+180x)


We get rid of parentheses

-216x^2-3x-180x+15=0

We add all the numbers together, and all the variables

-216x^2-183x+15=0

a = -216; b = -183; c = +15;
Δ = b2-4ac
Δ = -1832-4·(-216)·15
Δ = 46449
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:

$\sqrt{\Delta}=\sqrt{46449}=\sqrt{9*5161}=\sqrt{9}*\sqrt{5161}=3\sqrt{5161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-183)-3\sqrt{5161}}{2*-216}=\frac{183-3\sqrt{5161}}{-432}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-183)+3\sqrt{5161}}{2*-216}=\frac{183+3\sqrt{5161}}{-432}
$