x(5x-2)=2(9x+3)

Solution for x(5x-2)=2(9x+3) equation:

x(5x-2)=2(9x+3)

We move all terms to the left:

x(5x-2)-(2(9x+3))=0

We multiply parentheses

5x^2-2x-(2(9x+3))=0


We calculate terms in parentheses: -(2(9x+3)), so:

2(9x+3)

We multiply parentheses

18x+6

Back to the equation:

-(18x+6)


We get rid of parentheses

5x^2-2x-18x-6=0

We add all the numbers together, and all the variables

5x^2-20x-6=0

a = 5; b = -20; c = -6;
Δ = b2-4ac
Δ = -202-4·5·(-6)
Δ = 520
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:

$\sqrt{\Delta}=\sqrt{520}=\sqrt{4*130}=\sqrt{4}*\sqrt{130}=2\sqrt{130}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{130}}{2*5}=\frac{20-2\sqrt{130}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{130}}{2*5}=\frac{20+2\sqrt{130}}{10}
$