3x+10=7x+3x*(x-1)

Solution for 3x+10=7x+3x*(x-1) equation:

3x+10=7x+3x(x-1)

We move all terms to the left:

3x+10-(7x+3x(x-1))=0


We calculate terms in parentheses: -(7x+3x(x-1)), so:

7x+3x(x-1)

We multiply parentheses

3x^2+7x-3x

We add all the numbers together, and all the variables

3x^2+4x

Back to the equation:

-(3x^2+4x)


We get rid of parentheses

-3x^2+3x-4x+10=0

We add all the numbers together, and all the variables

-3x^2-1x+10=0

a = -3; b = -1; c = +10;
Δ = b2-4ac
Δ = -12-4·(-3)·10
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-11}{2*-3}=\frac{-10}{-6}
=1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+11}{2*-3}=\frac{12}{-6}
=-2
$