4x(7x+8)=5x(9x-20)

Solution for 4x(7x+8)=5x(9x-20) equation:

4x(7x+8)=5x(9x-20)

We move all terms to the left:

4x(7x+8)-(5x(9x-20))=0

We multiply parentheses

28x^2+32x-(5x(9x-20))=0


We calculate terms in parentheses: -(5x(9x-20)), so:

5x(9x-20)

We multiply parentheses

45x^2-100x

Back to the equation:

-(45x^2-100x)


We get rid of parentheses

28x^2-45x^2+32x+100x=0

We add all the numbers together, and all the variables

-17x^2+132x=0

a = -17; b = 132; c = 0;
Δ = b2-4ac
Δ = 1322-4·(-17)·0
Δ = 17424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{17424}=132$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(132)-132}{2*-17}=\frac{-264}{-34}
=7+13/17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(132)+132}{2*-17}=\frac{0}{-34}
=0
$