x^2+5,2x=78

Solution for x^2+5,2x=78 equation:

x^2+5.2x=78

We move all terms to the left:

x^2+5.2x-(78)=0

a = 1; b = 5.2; c = -78;
Δ = b2-4ac
Δ = 5.22-4·1·(-78)
Δ = 339.04
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{339.04}}{2*1}=\frac{-5.2-\sqrt{339.04}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5.2)+\sqrt{339.04}}{2*1}=\frac{-5.2+\sqrt{339.04}}{2}
$