-6x(6x-4)=-8(4x+3)

Solution for -6x(6x-4)=-8(4x+3) equation:

-6x(6x-4)=-8(4x+3)

We move all terms to the left:

-6x(6x-4)-(-8(4x+3))=0

We multiply parentheses

-36x^2+24x-(-8(4x+3))=0


We calculate terms in parentheses: -(-8(4x+3)), so:

-8(4x+3)

We multiply parentheses

-32x-24

Back to the equation:

-(-32x-24)


We get rid of parentheses

-36x^2+24x+32x+24=0

We add all the numbers together, and all the variables

-36x^2+56x+24=0

a = -36; b = 56; c = +24;
Δ = b2-4ac
Δ = 562-4·(-36)·24
Δ = 6592
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:

$\sqrt{\Delta}=\sqrt{6592}=\sqrt{64*103}=\sqrt{64}*\sqrt{103}=8\sqrt{103}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-8\sqrt{103}}{2*-36}=\frac{-56-8\sqrt{103}}{-72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+8\sqrt{103}}{2*-36}=\frac{-56+8\sqrt{103}}{-72}
$