4(x-1)2-2(x+2)2=-2x2+4x+11

Solution for 4(x-1)2-2(x+2)2=-2x2+4x+11 equation:

4(x-1)2-2(x+2)2=-2x^2+4x+11

We move all terms to the left:

4(x-1)2-2(x+2)2-(-2x^2+4x+11)=0

We multiply parentheses

-(-2x^2+4x+11)+8x-4x-8-8=0

We get rid of parentheses

2x^2-4x+8x-4x-11-8-8=0

We add all the numbers together, and all the variables

2x^2-27=0

a = 2; b = 0; c = -27;
Δ = b2-4ac
Δ = 02-4·2·(-27)
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{6}}{2*2}=\frac{0-6\sqrt{6}}{4}
=-\frac{6\sqrt{6}}{4}
=-\frac{3\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{6}}{2*2}=\frac{0+6\sqrt{6}}{4}
=\frac{6\sqrt{6}}{4}
=\frac{3\sqrt{6}}{2}
$