-2x+10=2x(-x+5)+1

Solution for -2x+10=2x(-x+5)+1 equation:

-2x+10=2x(-x+5)+1

We move all terms to the left:

-2x+10-(2x(-x+5)+1)=0

We add all the numbers together, and all the variables

-2x-(2x(-1x+5)+1)+10=0


We calculate terms in parentheses: -(2x(-1x+5)+1), so:

2x(-1x+5)+1

We multiply parentheses

-2x^2+10x+1

Back to the equation:

-(-2x^2+10x+1)


We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2-12x+9=0

a = 2; b = -12; c = +9;
Δ = b2-4ac
Δ = -122-4·2·9
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{2}}{2*2}=\frac{12-6\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{2}}{2*2}=\frac{12+6\sqrt{2}}{4}
$