2(x-3)5x=36

Solution for 2(x-3)5x=36 equation:

2(x-3)5x=36

We move all terms to the left:

2(x-3)5x-(36)=0

We multiply parentheses

10x^2-30x-36=0

a = 10; b = -30; c = -36;
Δ = b2-4ac
Δ = -302-4·10·(-36)
Δ = 2340
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:

$\sqrt{\Delta}=\sqrt{2340}=\sqrt{36*65}=\sqrt{36}*\sqrt{65}=6\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{65}}{2*10}=\frac{30-6\sqrt{65}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{65}}{2*10}=\frac{30+6\sqrt{65}}{20}
$