5x(2x+1)=7x(8x+4)

Solution for 5x(2x+1)=7x(8x+4) equation:

5x(2x+1)=7x(8x+4)

We move all terms to the left:

5x(2x+1)-(7x(8x+4))=0

We multiply parentheses

10x^2+5x-(7x(8x+4))=0


We calculate terms in parentheses: -(7x(8x+4)), so:

7x(8x+4)

We multiply parentheses

56x^2+28x

Back to the equation:

-(56x^2+28x)


We get rid of parentheses

10x^2-56x^2+5x-28x=0

We add all the numbers together, and all the variables

-46x^2-23x=0

a = -46; b = -23; c = 0;
Δ = b2-4ac
Δ = -232-4·(-46)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-23}{2*-46}=\frac{0}{-92}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+23}{2*-46}=\frac{46}{-92}
=-1/2
$