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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

x-5x-(7x(6x+8))+15+2=0


We calculate terms in parentheses: -(7x(6x+8)), so:

7x(6x+8)

We multiply parentheses

42x^2+56x

Back to the equation:

-(42x^2+56x)


We add all the numbers together, and all the variables

-4x-(42x^2+56x)+17=0

We get rid of parentheses

-42x^2-4x-56x+17=0

We add all the numbers together, and all the variables

-42x^2-60x+17=0

a = -42; b = -60; c = +17;
Δ = b2-4ac
Δ = -602-4·(-42)·17
Δ = 6456
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:

$\sqrt{\Delta}=\sqrt{6456}=\sqrt{4*1614}=\sqrt{4}*\sqrt{1614}=2\sqrt{1614}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{1614}}{2*-42}=\frac{60-2\sqrt{1614}}{-84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{1614}}{2*-42}=\frac{60+2\sqrt{1614}}{-84}
$