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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-5x^2+10x-(4x(2x-5)-(3x-4))=0


We calculate terms in parentheses: -(4x(2x-5)-(3x-4)), so:

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

We multiply parentheses

8x^2-20x-(3x-4)

We get rid of parentheses

8x^2-20x-3x+4

We add all the numbers together, and all the variables

8x^2-23x+4

Back to the equation:

-(8x^2-23x+4)


We get rid of parentheses

-5x^2-8x^2+10x+23x-4=0

We add all the numbers together, and all the variables

-13x^2+33x-4=0

a = -13; b = 33; c = -4;
Δ = b2-4ac
Δ = 332-4·(-13)·(-4)
Δ = 881
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{-(33)-\sqrt{881}}{2*-13}=\frac{-33-\sqrt{881}}{-26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+\sqrt{881}}{2*-13}=\frac{-33+\sqrt{881}}{-26}
$