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

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

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

We move all terms to the left:

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

We multiply parentheses

9x^2+63x-(8(x-7)+x)=0


We calculate terms in parentheses: -(8(x-7)+x), so:

8(x-7)+x

We add all the numbers together, and all the variables

x+8(x-7)

We multiply parentheses

x+8x-56

We add all the numbers together, and all the variables

9x-56

Back to the equation:

-(9x-56)


We get rid of parentheses

9x^2+63x-9x+56=0

We add all the numbers together, and all the variables

9x^2+54x+56=0

a = 9; b = 54; c = +56;
Δ = b2-4ac
Δ = 542-4·9·56
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-30}{2*9}=\frac{-84}{18}
=-4+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+30}{2*9}=\frac{-24}{18}
=-1+1/3
$