4+2x=3x(x-7)

Solution for 4+2x=3x(x-7) equation:

4+2x=3x(x-7)

We move all terms to the left:

4+2x-(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+4=0

We add all the numbers together, and all the variables

-3x^2+23x+4=0

a = -3; b = 23; c = +4;
Δ = b2-4ac
Δ = 232-4·(-3)·4
Δ = 577
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{577}}{2*-3}=\frac{-23-\sqrt{577}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{577}}{2*-3}=\frac{-23+\sqrt{577}}{-6}
$