X(x+1)+10=10x

Solution for X(x+1)+10=10x equation:

X(X+1)+10=10X

We move all terms to the left:

X(X+1)+10-(10X)=0

We add all the numbers together, and all the variables

-10X+X(X+1)+10=0

We multiply parentheses

X^2-10X+X+10=0

We add all the numbers together, and all the variables

X^2-9X+10=0

a = 1; b = -9; c = +10;
Δ = b2-4ac
Δ = -92-4·1·10
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{41}}{2*1}=\frac{9-\sqrt{41}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{41}}{2*1}=\frac{9+\sqrt{41}}{2}
$