4x+12x-6=4(4x+7)4x

Solution for 4x+12x-6=4(4x+7)4x equation:

4x+12x-6=4(4x+7)4x

We move all terms to the left:

4x+12x-6-(4(4x+7)4x)=0

We add all the numbers together, and all the variables

16x-(4(4x+7)4x)-6=0


We calculate terms in parentheses: -(4(4x+7)4x), so:

4(4x+7)4x

We multiply parentheses

64x^2+112x

Back to the equation:

-(64x^2+112x)


We get rid of parentheses

-64x^2+16x-112x-6=0

We add all the numbers together, and all the variables

-64x^2-96x-6=0

a = -64; b = -96; c = -6;
Δ = b2-4ac
Δ = -962-4·(-64)·(-6)
Δ = 7680
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:

$\sqrt{\Delta}=\sqrt{7680}=\sqrt{256*30}=\sqrt{256}*\sqrt{30}=16\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-16\sqrt{30}}{2*-64}=\frac{96-16\sqrt{30}}{-128}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+16\sqrt{30}}{2*-64}=\frac{96+16\sqrt{30}}{-128}
$