x^2+3x-11=54

Solution for x^2+3x-11=54 equation:

x^2+3x-11=54

We move all terms to the left:

x^2+3x-11-(54)=0

We add all the numbers together, and all the variables

x^2+3x-65=0

a = 1; b = 3; c = -65;
Δ = b2-4ac
Δ = 32-4·1·(-65)
Δ = 269
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{-(3)-\sqrt{269}}{2*1}=\frac{-3-\sqrt{269}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{269}}{2*1}=\frac{-3+\sqrt{269}}{2}
$