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

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

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

We move all terms to the left:

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

We multiply parentheses

7x-(3(x-1)x)+21=0


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

3(x-1)x

We multiply parentheses

3x^2-3x

Back to the equation:

-(3x^2-3x)


We get rid of parentheses

-3x^2+7x+3x+21=0

We add all the numbers together, and all the variables

-3x^2+10x+21=0

a = -3; b = 10; c = +21;
Δ = b2-4ac
Δ = 102-4·(-3)·21
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4\sqrt{22}}{2*-3}=\frac{-10-4\sqrt{22}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4\sqrt{22}}{2*-3}=\frac{-10+4\sqrt{22}}{-6}
$