-x2+18x=5-4x2

Solution for -x2+18x=5-4x2 equation:

-x2+18x=5-4x^2

We move all terms to the left:

-x2+18x-(5-4x^2)=0

We add all the numbers together, and all the variables

-1x^2-(5-4x^2)+18x=0

We get rid of parentheses

-1x^2+4x^2+18x-5=0

We add all the numbers together, and all the variables

3x^2+18x-5=0

a = 3; b = 18; c = -5;
Δ = b2-4ac
Δ = 182-4·3·(-5)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-8\sqrt{6}}{2*3}=\frac{-18-8\sqrt{6}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+8\sqrt{6}}{2*3}=\frac{-18+8\sqrt{6}}{6}
$