4x(5x-2)=2(9x+3)

Solution for 4x(5x-2)=2(9x+3) equation:

4x(5x-2)=2(9x+3)

We move all terms to the left:

4x(5x-2)-(2(9x+3))=0

We multiply parentheses

20x^2-8x-(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

20x^2-8x-18x-6=0

We add all the numbers together, and all the variables

20x^2-26x-6=0

a = 20; b = -26; c = -6;
Δ = b2-4ac
Δ = -262-4·20·(-6)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-34}{2*20}=\frac{-8}{40}
=-1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+34}{2*20}=\frac{60}{40}
=1+1/2
$