4x-1=2(2x-3)5x

Solution for 4x-1=2(2x-3)5x equation:

4x-1=2(2x-3)5x

We move all terms to the left:

4x-1-(2(2x-3)5x)=0


We calculate terms in parentheses: -(2(2x-3)5x), so:

2(2x-3)5x

We multiply parentheses

20x^2-30x

Back to the equation:

-(20x^2-30x)


We get rid of parentheses

-20x^2+4x+30x-1=0

We add all the numbers together, and all the variables

-20x^2+34x-1=0

a = -20; b = 34; c = -1;
Δ = b2-4ac
Δ = 342-4·(-20)·(-1)
Δ = 1076
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:

$\sqrt{\Delta}=\sqrt{1076}=\sqrt{4*269}=\sqrt{4}*\sqrt{269}=2\sqrt{269}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{269}}{2*-20}=\frac{-34-2\sqrt{269}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{269}}{2*-20}=\frac{-34+2\sqrt{269}}{-40}
$