13-3x=4x(x-2)

Solution for 13-3x=4x(x-2) equation:

13-3x=4x(x-2)

We move all terms to the left:

13-3x-(4x(x-2))=0


We calculate terms in parentheses: -(4x(x-2)), so:

4x(x-2)

We multiply parentheses

4x^2-8x

Back to the equation:

-(4x^2-8x)


We get rid of parentheses

-4x^2-3x+8x+13=0

We add all the numbers together, and all the variables

-4x^2+5x+13=0

a = -4; b = 5; c = +13;
Δ = b2-4ac
Δ = 52-4·(-4)·13
Δ = 233
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{233}}{2*-4}=\frac{-5-\sqrt{233}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{233}}{2*-4}=\frac{-5+\sqrt{233}}{-8}
$