-3x(7x+4)=-4(3x+1)

Solution for -3x(7x+4)=-4(3x+1) equation:

-3x(7x+4)=-4(3x+1)

We move all terms to the left:

-3x(7x+4)-(-4(3x+1))=0

We multiply parentheses

-21x^2-12x-(-4(3x+1))=0


We calculate terms in parentheses: -(-4(3x+1)), so:

-4(3x+1)

We multiply parentheses

-12x-4

Back to the equation:

-(-12x-4)


We get rid of parentheses

-21x^2-12x+12x+4=0

We add all the numbers together, and all the variables

-21x^2+4=0

a = -21; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-21)·4
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{21}}{2*-21}=\frac{0-4\sqrt{21}}{-42}
=-\frac{4\sqrt{21}}{-42}
=-\frac{2\sqrt{21}}{-21}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{21}}{2*-21}=\frac{0+4\sqrt{21}}{-42}
=\frac{4\sqrt{21}}{-42}
=\frac{2\sqrt{21}}{-21}
$