2x+75x+8=3(5+6x)12x

Solution for 2x+75x+8=3(5+6x)12x equation:

2x+75x+8=3(5+6x)12x

We move all terms to the left:

2x+75x+8-(3(5+6x)12x)=0

We add all the numbers together, and all the variables

2x+75x-(3(6x+5)12x)+8=0

We add all the numbers together, and all the variables

77x-(3(6x+5)12x)+8=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+77x-180x+8=0

We add all the numbers together, and all the variables

-216x^2-103x+8=0

a = -216; b = -103; c = +8;
Δ = b2-4ac
Δ = -1032-4·(-216)·8
Δ = 17521
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{-(-103)-\sqrt{17521}}{2*-216}=\frac{103-\sqrt{17521}}{-432}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-103)+\sqrt{17521}}{2*-216}=\frac{103+\sqrt{17521}}{-432}
$