4x^2=2+18x

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

4x^2=2+18x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

4x^2-18x-2=0

a = 4; b = -18; c = -2;
Δ = b2-4ac
Δ = -182-4·4·(-2)
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{89}}{2*4}=\frac{18-2\sqrt{89}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{89}}{2*4}=\frac{18+2\sqrt{89}}{8}
$