31.2x+15.6x^2=5.2

Solution for 31.2x+15.6x^2=5.2 equation:

31.2x+15.6x^2=5.2

We move all terms to the left:

31.2x+15.6x^2-(5.2)=0

We add all the numbers together, and all the variables

15.6x^2+31.2x-5.2=0

a = 15.6; b = 31.2; c = -5.2;
Δ = b2-4ac
Δ = 31.22-4·15.6·(-5.2)
Δ = 1297.92
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{-(31.2)-\sqrt{1297.92}}{2*15.6}=\frac{-31.2-\sqrt{1297.92}}{31.2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31.2)+\sqrt{1297.92}}{2*15.6}=\frac{-31.2+\sqrt{1297.92}}{31.2}
$