9=10(x-2)3x

Solution for 9=10(x-2)3x equation:

9=10(x-2)3x

We move all terms to the left:

9-(10(x-2)3x)=0


We calculate terms in parentheses: -(10(x-2)3x), so:

10(x-2)3x

We multiply parentheses

30x^2-60x

Back to the equation:

-(30x^2-60x)


We get rid of parentheses

-30x^2+60x+9=0

a = -30; b = 60; c = +9;
Δ = b2-4ac
Δ = 602-4·(-30)·9
Δ = 4680
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:

$\sqrt{\Delta}=\sqrt{4680}=\sqrt{36*130}=\sqrt{36}*\sqrt{130}=6\sqrt{130}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-6\sqrt{130}}{2*-30}=\frac{-60-6\sqrt{130}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+6\sqrt{130}}{2*-30}=\frac{-60+6\sqrt{130}}{-60}
$