3x-2x=x(3x-5)-85

Solution for 3x-2x=x(3x-5)-85 equation:

3x-2x=x(3x-5)-85

We move all terms to the left:

3x-2x-(x(3x-5)-85)=0

We add all the numbers together, and all the variables

x-(x(3x-5)-85)=0


We calculate terms in parentheses: -(x(3x-5)-85), so:

x(3x-5)-85

We multiply parentheses

3x^2-5x-85

Back to the equation:

-(3x^2-5x-85)


We get rid of parentheses

-3x^2+x+5x+85=0

We add all the numbers together, and all the variables

-3x^2+6x+85=0

a = -3; b = 6; c = +85;
Δ = b2-4ac
Δ = 62-4·(-3)·85
Δ = 1056
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:

$\sqrt{\Delta}=\sqrt{1056}=\sqrt{16*66}=\sqrt{16}*\sqrt{66}=4\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{66}}{2*-3}=\frac{-6-4\sqrt{66}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{66}}{2*-3}=\frac{-6+4\sqrt{66}}{-6}
$