2x(9x-9)-63=4x(3x-42)+193

Solution for 2x(9x-9)-63=4x(3x-42)+193 equation:

2x(9x-9)-63=4x(3x-42)+193

We move all terms to the left:

2x(9x-9)-63-(4x(3x-42)+193)=0

We multiply parentheses

18x^2-18x-(4x(3x-42)+193)-63=0


We calculate terms in parentheses: -(4x(3x-42)+193), so:

4x(3x-42)+193

We multiply parentheses

12x^2-168x+193

Back to the equation:

-(12x^2-168x+193)


We get rid of parentheses

18x^2-12x^2-18x+168x-193-63=0

We add all the numbers together, and all the variables

6x^2+150x-256=0

a = 6; b = 150; c = -256;
Δ = b2-4ac
Δ = 1502-4·6·(-256)
Δ = 28644
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:

$\sqrt{\Delta}=\sqrt{28644}=\sqrt{4*7161}=\sqrt{4}*\sqrt{7161}=2\sqrt{7161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-2\sqrt{7161}}{2*6}=\frac{-150-2\sqrt{7161}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+2\sqrt{7161}}{2*6}=\frac{-150+2\sqrt{7161}}{12}
$