10x+2x^2=208

Solution for 10x+2x^2=208 equation:

10x+2x^2=208

We move all terms to the left:

10x+2x^2-(208)=0

a = 2; b = 10; c = -208;
Δ = b2-4ac
Δ = 102-4·2·(-208)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-42}{2*2}=\frac{-52}{4}
=-13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+42}{2*2}=\frac{32}{4}
=8
$