4x(5x+7)=4(5x+8x+4)

Solution for 4x(5x+7)=4(5x+8x+4) equation:

4x(5x+7)=4(5x+8x+4)

We move all terms to the left:

4x(5x+7)-(4(5x+8x+4))=0

We add all the numbers together, and all the variables

4x(5x+7)-(4(13x+4))=0

We multiply parentheses

20x^2+28x-(4(13x+4))=0


We calculate terms in parentheses: -(4(13x+4)), so:

4(13x+4)

We multiply parentheses

52x+16

Back to the equation:

-(52x+16)


We get rid of parentheses

20x^2+28x-52x-16=0

We add all the numbers together, and all the variables

20x^2-24x-16=0

a = 20; b = -24; c = -16;
Δ = b2-4ac
Δ = -242-4·20·(-16)
Δ = 1856
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:

$\sqrt{\Delta}=\sqrt{1856}=\sqrt{64*29}=\sqrt{64}*\sqrt{29}=8\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{29}}{2*20}=\frac{24-8\sqrt{29}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{29}}{2*20}=\frac{24+8\sqrt{29}}{40}
$