X.5(x+9)-4=51

Solution for X.5(x+9)-4=51 equation:

X.5(X+9)-4=51

We move all terms to the left:

X.5(X+9)-4-(51)=0

We add all the numbers together, and all the variables

X.5(X+9)-55=0

We multiply parentheses

X^2+9X-55=0

a = 1; b = 9; c = -55;
Δ = b2-4ac
Δ = 92-4·1·(-55)
Δ = 301
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{-(9)-\sqrt{301}}{2*1}=\frac{-9-\sqrt{301}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{301}}{2*1}=\frac{-9+\sqrt{301}}{2}
$