34+x=0.2x^2

Solution for 34+x=0.2x^2 equation:

34+x=0.2x^2

We move all terms to the left:

34+x-(0.2x^2)=0

We get rid of parentheses

-0.2x^2+x+34=0

a = -0.2; b = 1; c = +34;
Δ = b2-4ac
Δ = 12-4·(-0.2)·34
Δ = 28.2
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{28.2}}{2*-0.2}=\frac{-1-\sqrt{28.2}}{-0.4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{28.2}}{2*-0.2}=\frac{-1+\sqrt{28.2}}{-0.4}
$