3x(x+7)=4x(x+5x-3)

Solution for 3x(x+7)=4x(x+5x-3) equation:

3x(x+7)=4x(x+5x-3)

We move all terms to the left:

3x(x+7)-(4x(x+5x-3))=0

We add all the numbers together, and all the variables

3x(x+7)-(4x(6x-3))=0

We multiply parentheses

3x^2+21x-(4x(6x-3))=0


We calculate terms in parentheses: -(4x(6x-3)), so:

4x(6x-3)

We multiply parentheses

24x^2-12x

Back to the equation:

-(24x^2-12x)


We get rid of parentheses

3x^2-24x^2+21x+12x=0

We add all the numbers together, and all the variables

-21x^2+33x=0

a = -21; b = 33; c = 0;
Δ = b2-4ac
Δ = 332-4·(-21)·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-33}{2*-21}=\frac{-66}{-42}
=1+4/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+33}{2*-21}=\frac{0}{-42}
=0
$