2x^2+11x=x^2-3x-28

Solution for 2x^2+11x=x^2-3x-28 equation:

2x^2+11x=x^2-3x-28

We move all terms to the left:

2x^2+11x-(x^2-3x-28)=0

We get rid of parentheses

2x^2-x^2+11x+3x+28=0

We add all the numbers together, and all the variables

x^2+14x+28=0

a = 1; b = 14; c = +28;
Δ = b2-4ac
Δ = 142-4·1·28
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{21}}{2*1}=\frac{-14-2\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{21}}{2*1}=\frac{-14+2\sqrt{21}}{2}
$