-7x-3(9-7x)x=-4

Solution for -7x-3(9-7x)x=-4 equation:

-7x-3(9-7x)x=-4

We move all terms to the left:

-7x-3(9-7x)x-(-4)=0

We add all the numbers together, and all the variables

-7x-3(-7x+9)x-(-4)=0

We add all the numbers together, and all the variables

-7x-3(-7x+9)x+4=0

We multiply parentheses

21x^2-7x-27x+4=0

We add all the numbers together, and all the variables

21x^2-34x+4=0

a = 21; b = -34; c = +4;
Δ = b2-4ac
Δ = -342-4·21·4
Δ = 820
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:

$\sqrt{\Delta}=\sqrt{820}=\sqrt{4*205}=\sqrt{4}*\sqrt{205}=2\sqrt{205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{205}}{2*21}=\frac{34-2\sqrt{205}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{205}}{2*21}=\frac{34+2\sqrt{205}}{42}
$