2x+7=3x(x-7)

Solution for 2x+7=3x(x-7) equation:

2x+7=3x(x-7)

We move all terms to the left:

2x+7-(3x(x-7))=0


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

3x(x-7)

We multiply parentheses

3x^2-21x

Back to the equation:

-(3x^2-21x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-3x^2+23x+7=0

a = -3; b = 23; c = +7;
Δ = b2-4ac
Δ = 232-4·(-3)·7
Δ = 613
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{-(23)-\sqrt{613}}{2*-3}=\frac{-23-\sqrt{613}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{613}}{2*-3}=\frac{-23+\sqrt{613}}{-6}
$