390^2=(3x+4)*x

Solution for 390^2=(3x+4)*x equation:

390^2=(3x+4)*x

We move all terms to the left:

390^2-((3x+4)*x)=0

We add all the numbers together, and all the variables

-((3x+4)*x)+152100=0


We calculate terms in parentheses: -((3x+4)*x), so:

(3x+4)*x

We multiply parentheses

3x^2+4x

Back to the equation:

-(3x^2+4x)


We get rid of parentheses

-3x^2-4x+152100=0

a = -3; b = -4; c = +152100;
Δ = b2-4ac
Δ = -42-4·(-3)·152100
Δ = 1825216
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:

$\sqrt{\Delta}=\sqrt{1825216}=\sqrt{23104*79}=\sqrt{23104}*\sqrt{79}=152\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-152\sqrt{79}}{2*-3}=\frac{4-152\sqrt{79}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+152\sqrt{79}}{2*-3}=\frac{4+152\sqrt{79}}{-6}
$