(5x-9)(3x+5)=8(5x-9)(-2x+1)

Solution for (5x-9)(3x+5)=8(5x-9)(-2x+1) equation:

(5x-9)(3x+5)=8(5x-9)(-2x+1)

We move all terms to the left:

(5x-9)(3x+5)-(8(5x-9)(-2x+1))=0

We multiply parentheses ..

(+15x^2+25x-27x-45)-(8(5x-9)(-2x+1))=0


We calculate terms in parentheses: -(8(5x-9)(-2x+1)), so:

8(5x-9)(-2x+1)

We multiply parentheses ..

8(-10x^2+5x+18x-9)

We multiply parentheses

-80x^2+40x+144x-72

We add all the numbers together, and all the variables

-80x^2+184x-72

Back to the equation:

-(-80x^2+184x-72)


We get rid of parentheses

15x^2+80x^2+25x-27x-184x-45+72=0

We add all the numbers together, and all the variables

95x^2-186x+27=0

a = 95; b = -186; c = +27;
Δ = b2-4ac
Δ = -1862-4·95·27
Δ = 24336
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{24336}=156$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-186)-156}{2*95}=\frac{30}{190}
=3/19
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-186)+156}{2*95}=\frac{342}{190}
=1+4/5
$