4x(2x-9)=5(6-x)

Solution for 4x(2x-9)=5(6-x) equation:

4x(2x-9)=5(6-x)

We move all terms to the left:

4x(2x-9)-(5(6-x))=0

We add all the numbers together, and all the variables

4x(2x-9)-(5(-1x+6))=0

We multiply parentheses

8x^2-36x-(5(-1x+6))=0


We calculate terms in parentheses: -(5(-1x+6)), so:

5(-1x+6)

We multiply parentheses

-5x+30

Back to the equation:

-(-5x+30)


We get rid of parentheses

8x^2-36x+5x-30=0

We add all the numbers together, and all the variables

8x^2-31x-30=0

a = 8; b = -31; c = -30;
Δ = b2-4ac
Δ = -312-4·8·(-30)
Δ = 1921
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{-(-31)-\sqrt{1921}}{2*8}=\frac{31-\sqrt{1921}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+\sqrt{1921}}{2*8}=\frac{31+\sqrt{1921}}{16}
$