4x(x-6)=2(7+3x)

Solution for 4x(x-6)=2(7+3x) equation:

4x(x-6)=2(7+3x)

We move all terms to the left:

4x(x-6)-(2(7+3x))=0

We add all the numbers together, and all the variables

4x(x-6)-(2(3x+7))=0

We multiply parentheses

4x^2-24x-(2(3x+7))=0


We calculate terms in parentheses: -(2(3x+7)), so:

2(3x+7)

We multiply parentheses

6x+14

Back to the equation:

-(6x+14)


We get rid of parentheses

4x^2-24x-6x-14=0

We add all the numbers together, and all the variables

4x^2-30x-14=0

a = 4; b = -30; c = -14;
Δ = b2-4ac
Δ = -302-4·4·(-14)
Δ = 1124
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:

$\sqrt{\Delta}=\sqrt{1124}=\sqrt{4*281}=\sqrt{4}*\sqrt{281}=2\sqrt{281}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{281}}{2*4}=\frac{30-2\sqrt{281}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{281}}{2*4}=\frac{30+2\sqrt{281}}{8}
$