6x+19=(2-x)(2-x)

Solution for 6x+19=(2-x)(2-x) equation:

6x+19=(2-x)(2-x)

We move all terms to the left:

6x+19-((2-x)(2-x))=0

We add all the numbers together, and all the variables

6x-((-1x+2)(-1x+2))+19=0

We multiply parentheses ..

-((+x^2-2x-2x+4))+6x+19=0


We calculate terms in parentheses: -((+x^2-2x-2x+4)), so:

(+x^2-2x-2x+4)

We get rid of parentheses

x^2-2x-2x+4

We add all the numbers together, and all the variables

x^2-4x+4

Back to the equation:

-(x^2-4x+4)


We add all the numbers together, and all the variables

6x-(x^2-4x+4)+19=0

We get rid of parentheses

-x^2+6x+4x-4+19=0

We add all the numbers together, and all the variables

-1x^2+10x+15=0

a = -1; b = 10; c = +15;
Δ = b2-4ac
Δ = 102-4·(-1)·15
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4\sqrt{10}}{2*-1}=\frac{-10-4\sqrt{10}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4\sqrt{10}}{2*-1}=\frac{-10+4\sqrt{10}}{-2}
$