34x+4x^2=-18

Solution for 34x+4x^2=-18 equation:

34x+4x^2=-18

We move all terms to the left:

34x+4x^2-(-18)=0

We add all the numbers together, and all the variables

4x^2+34x+18=0

a = 4; b = 34; c = +18;
Δ = b2-4ac
Δ = 342-4·4·18
Δ = 868
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{868}=\sqrt{4*217}=\sqrt{4}*\sqrt{217}=2\sqrt{217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{217}}{2*4}=\frac{-34-2\sqrt{217}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{217}}{2*4}=\frac{-34+2\sqrt{217}}{8}
$