(4x+9)(x-1)=5x

Solution for (4x+9)(x-1)=5x equation:

(4x+9)(x-1)=5x

We move all terms to the left:

(4x+9)(x-1)-(5x)=0

We add all the numbers together, and all the variables

-5x+(4x+9)(x-1)=0

We multiply parentheses ..

(+4x^2-4x+9x-9)-5x=0

We get rid of parentheses

4x^2-4x+9x-5x-9=0

We add all the numbers together, and all the variables

4x^2-9=0

a = 4; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·4·(-9)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*4}=\frac{-12}{8}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*4}=\frac{12}{8}
=1+1/2
$