9x(x+7)=6x+8

Solution for 9x(x+7)=6x+8 equation:

9x(x+7)=6x+8

We move all terms to the left:

9x(x+7)-(6x+8)=0

We multiply parentheses

9x^2+63x-(6x+8)=0

We get rid of parentheses

9x^2+63x-6x-8=0

We add all the numbers together, and all the variables

9x^2+57x-8=0

a = 9; b = 57; c = -8;
Δ = b2-4ac
Δ = 572-4·9·(-8)
Δ = 3537
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:

$\sqrt{\Delta}=\sqrt{3537}=\sqrt{9*393}=\sqrt{9}*\sqrt{393}=3\sqrt{393}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(57)-3\sqrt{393}}{2*9}=\frac{-57-3\sqrt{393}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(57)+3\sqrt{393}}{2*9}=\frac{-57+3\sqrt{393}}{18}
$