X+8.3x2=7.1

Solution for X+8.3x2=7.1 equation:

X+8.3X^2=7.1

We move all terms to the left:

X+8.3X^2-(7.1)=0

We add all the numbers together, and all the variables

8.3X^2+X-7.1=0

a = 8.3; b = 1; c = -7.1;
Δ = b2-4ac
Δ = 12-4·8.3·(-7.1)
Δ = 236.72
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{-(1)-\sqrt{236.72}}{2*8.3}=\frac{-1-\sqrt{236.72}}{16.6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{236.72}}{2*8.3}=\frac{-1+\sqrt{236.72}}{16.6}
$