(2x-1)2+2(x-3)2=-2(x2+1)+15

Solution for (2x-1)2+2(x-3)2=-2(x2+1)+15 equation:

(2x-1)2+2(x-3)2=-2(x2+1)+15

We move all terms to the left:

(2x-1)2+2(x-3)2-(-2(x2+1)+15)=0

We add all the numbers together, and all the variables

-(-2(+x^2+1)+15)+(2x-1)2+2(x-3)2=0

We multiply parentheses

-(-2(+x^2+1)+15)+4x+4x-2-12=0


We calculate terms in parentheses: -(-2(+x^2+1)+15), so:

-2(+x^2+1)+15

We multiply parentheses

-2x^2-2+15

We add all the numbers together, and all the variables

-2x^2+13

Back to the equation:

-(-2x^2+13)


We add all the numbers together, and all the variables

-(-2x^2+13)+8x-14=0

We get rid of parentheses

2x^2+8x-13-14=0

We add all the numbers together, and all the variables

2x^2+8x-27=0

a = 2; b = 8; c = -27;
Δ = b2-4ac
Δ = 82-4·2·(-27)
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{70}}{2*2}=\frac{-8-2\sqrt{70}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{70}}{2*2}=\frac{-8+2\sqrt{70}}{4}
$