x2+5x=3x+11

Solution for x2+5x=3x+11 equation:

x2+5x=3x+11

We move all terms to the left:

x2+5x-(3x+11)=0

We add all the numbers together, and all the variables

x^2+5x-(3x+11)=0

We get rid of parentheses

x^2+5x-3x-11=0

We add all the numbers together, and all the variables

x^2+2x-11=0

a = 1; b = 2; c = -11;
Δ = b2-4ac
Δ = 22-4·1·(-11)
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{3}}{2*1}=\frac{-2-4\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{3}}{2*1}=\frac{-2+4\sqrt{3}}{2}
$