4x^2+18x+5=5-2x^2

Solution for 4x^2+18x+5=5-2x^2 equation:

4x^2+18x+5=5-2x^2

We move all terms to the left:

4x^2+18x+5-(5-2x^2)=0

We get rid of parentheses

4x^2+2x^2+18x-5+5=0

We add all the numbers together, and all the variables

6x^2+18x=0

a = 6; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·6·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*6}=\frac{-36}{12}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*6}=\frac{0}{12}
=0
$