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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We multiply parentheses ..

-((+9x^2+4x-45x-20))+9x-4=0


We calculate terms in parentheses: -((+9x^2+4x-45x-20)), so:

(+9x^2+4x-45x-20)

We get rid of parentheses

9x^2+4x-45x-20

We add all the numbers together, and all the variables

9x^2-41x-20

Back to the equation:

-(9x^2-41x-20)


We add all the numbers together, and all the variables

9x-(9x^2-41x-20)-4=0

We get rid of parentheses

-9x^2+9x+41x+20-4=0

We add all the numbers together, and all the variables

-9x^2+50x+16=0

a = -9; b = 50; c = +16;
Δ = b2-4ac
Δ = 502-4·(-9)·16
Δ = 3076
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:

$\sqrt{\Delta}=\sqrt{3076}=\sqrt{4*769}=\sqrt{4}*\sqrt{769}=2\sqrt{769}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{769}}{2*-9}=\frac{-50-2\sqrt{769}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{769}}{2*-9}=\frac{-50+2\sqrt{769}}{-18}
$