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

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

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

We move all terms to the left:

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

We multiply parentheses

9x^2+2x-9x-(8(2x+2)-5)=0


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

8(2x+2)-5

We multiply parentheses

16x+16-5

We add all the numbers together, and all the variables

16x+11

Back to the equation:

-(16x+11)


We add all the numbers together, and all the variables

9x^2-7x-(16x+11)=0

We get rid of parentheses

9x^2-7x-16x-11=0

We add all the numbers together, and all the variables

9x^2-23x-11=0

a = 9; b = -23; c = -11;
Δ = b2-4ac
Δ = -232-4·9·(-11)
Δ = 925
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:

$\sqrt{\Delta}=\sqrt{925}=\sqrt{25*37}=\sqrt{25}*\sqrt{37}=5\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-5\sqrt{37}}{2*9}=\frac{23-5\sqrt{37}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+5\sqrt{37}}{2*9}=\frac{23+5\sqrt{37}}{18}
$