(x2+5)-6=(9x+18)3

Solution for (x2+5)-6=(9x+18)3 equation:

(x2+5)-6=(9x+18)3

We move all terms to the left:

(x2+5)-6-((9x+18)3)=0

We add all the numbers together, and all the variables

(+x^2+5)-((9x+18)3)-6=0

We get rid of parentheses

x^2-((9x+18)3)+5-6=0


We calculate terms in parentheses: -((9x+18)3), so:

(9x+18)3

We multiply parentheses

27x+54

Back to the equation:

-(27x+54)


We add all the numbers together, and all the variables

x^2-(27x+54)-1=0

We get rid of parentheses

x^2-27x-54-1=0

We add all the numbers together, and all the variables

x^2-27x-55=0

a = 1; b = -27; c = -55;
Δ = b2-4ac
Δ = -272-4·1·(-55)
Δ = 949
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{-(-27)-\sqrt{949}}{2*1}=\frac{27-\sqrt{949}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{949}}{2*1}=\frac{27+\sqrt{949}}{2}
$