5x(7x+4)=4x(9x-20)

Solution for 5x(7x+4)=4x(9x-20) equation:

5x(7x+4)=4x(9x-20)

We move all terms to the left:

5x(7x+4)-(4x(9x-20))=0

We multiply parentheses

35x^2+20x-(4x(9x-20))=0


We calculate terms in parentheses: -(4x(9x-20)), so:

4x(9x-20)

We multiply parentheses

36x^2-80x

Back to the equation:

-(36x^2-80x)


We get rid of parentheses

35x^2-36x^2+20x+80x=0

We add all the numbers together, and all the variables

-1x^2+100x=0

a = -1; b = 100; c = 0;
Δ = b2-4ac
Δ = 1002-4·(-1)·0
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-100}{2*-1}=\frac{-200}{-2}
=+100
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+100}{2*-1}=\frac{0}{-2}
=0
$