(x+3)=x(3x-91)

Solution for (x+3)=x(3x-91) equation:

(x+3)=x(3x-91)

We move all terms to the left:

(x+3)-(x(3x-91))=0

We get rid of parentheses

x-(x(3x-91))+3=0


We calculate terms in parentheses: -(x(3x-91)), so:

x(3x-91)

We multiply parentheses

3x^2-91x

Back to the equation:

-(3x^2-91x)


We get rid of parentheses

-3x^2+x+91x+3=0

We add all the numbers together, and all the variables

-3x^2+92x+3=0

a = -3; b = 92; c = +3;
Δ = b2-4ac
Δ = 922-4·(-3)·3
Δ = 8500
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:

$\sqrt{\Delta}=\sqrt{8500}=\sqrt{100*85}=\sqrt{100}*\sqrt{85}=10\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(92)-10\sqrt{85}}{2*-3}=\frac{-92-10\sqrt{85}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(92)+10\sqrt{85}}{2*-3}=\frac{-92+10\sqrt{85}}{-6}
$