-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+18x-14=0

a = -4; b = 18; c = -14;
Δ = b2-4ac
Δ = 182-4·(-4)·(-14)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-10}{2*-4}=\frac{-28}{-8}
=3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+10}{2*-4}=\frac{-8}{-8}
=1
$