X(x+5.2)=51

Solution for X(x+5.2)=51 equation:

X(X+5.2)=51

We move all terms to the left:

X(X+5.2)-(51)=0

We multiply parentheses

X^2+5.2X-51=0

a = 1; b = 5.2; c = -51;
Δ = b2-4ac
Δ = 5.22-4·1·(-51)
Δ = 231.04
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{-(5.2)-\sqrt{231.04}}{2*1}=\frac{-5.2-\sqrt{231.04}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5.2)+\sqrt{231.04}}{2*1}=\frac{-5.2+\sqrt{231.04}}{2}
$