9x(x-3)+8=7x+11

Solution for 9x(x-3)+8=7x+11 equation:

9x(x-3)+8=7x+11

We move all terms to the left:

9x(x-3)+8-(7x+11)=0

We multiply parentheses

9x^2-27x-(7x+11)+8=0

We get rid of parentheses

9x^2-27x-7x-11+8=0

We add all the numbers together, and all the variables

9x^2-34x-3=0

a = 9; b = -34; c = -3;
Δ = b2-4ac
Δ = -342-4·9·(-3)
Δ = 1264
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:

$\sqrt{\Delta}=\sqrt{1264}=\sqrt{16*79}=\sqrt{16}*\sqrt{79}=4\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-4\sqrt{79}}{2*9}=\frac{34-4\sqrt{79}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+4\sqrt{79}}{2*9}=\frac{34+4\sqrt{79}}{18}
$