X(8+x)=3.5(6+3.5)

Solution for X(8+x)=3.5(6+3.5) equation:

X(8+X)=3.5(6+3.5)

We move all terms to the left:

X(8+X)-(3.5(6+3.5))=0

We add all the numbers together, and all the variables

X(X+8)-(3.5(9.5))=0

We add all the numbers together, and all the variables

X(X+8)-33.25=0

We multiply parentheses

X^2+8X-33.25=0

a = 1; b = 8; c = -33.25;
Δ = b2-4ac
Δ = 82-4·1·(-33.25)
Δ = 197
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{197}}{2*1}=\frac{-8-\sqrt{197}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+\sqrt{197}}{2*1}=\frac{-8+\sqrt{197}}{2}
$