10.33=8.5x(1+X)

Solution for 10.33=8.5x(1+X) equation:

10.33=8.5x(1+x)

We move all terms to the left:

10.33-(8.5x(1+x))=0

We add all the numbers together, and all the variables

-(8.5x(x+1))+10.33=0


We calculate terms in parentheses: -(8.5x(x+1)), so:

8.5x(x+1)

We multiply parentheses

8x^2+8x

Back to the equation:

-(8x^2+8x)


We get rid of parentheses

-8x^2-8x+10.33=0

a = -8; b = -8; c = +10.33;
Δ = b2-4ac
Δ = -82-4·(-8)·10.33
Δ = 394.56
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-\sqrt{394.56}}{2*-8}=\frac{8-\sqrt{394.56}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+\sqrt{394.56}}{2*-8}=\frac{8+\sqrt{394.56}}{-16}
$