x(x+2)-10=x(7-2x)

Solution for x(x+2)-10=x(7-2x) equation:

x(x+2)-10=x(7-2x)

We move all terms to the left:

x(x+2)-10-(x(7-2x))=0

We add all the numbers together, and all the variables

x(x+2)-(x(-2x+7))-10=0

We multiply parentheses

x^2+2x-(x(-2x+7))-10=0


We calculate terms in parentheses: -(x(-2x+7)), so:

x(-2x+7)

We multiply parentheses

-2x^2+7x

Back to the equation:

-(-2x^2+7x)


We get rid of parentheses

x^2+2x^2-7x+2x-10=0

We add all the numbers together, and all the variables

3x^2-5x-10=0

a = 3; b = -5; c = -10;
Δ = b2-4ac
Δ = -52-4·3·(-10)
Δ = 145
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{-(-5)-\sqrt{145}}{2*3}=\frac{5-\sqrt{145}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{145}}{2*3}=\frac{5+\sqrt{145}}{6}
$