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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-1x^2+5x+2x-10)-((x+6)(x-4))=0


We calculate terms in parentheses: -((x+6)(x-4)), so:

(x+6)(x-4)

We multiply parentheses ..

(+x^2-4x+6x-24)

We get rid of parentheses

x^2-4x+6x-24

We add all the numbers together, and all the variables

x^2+2x-24

Back to the equation:

-(x^2+2x-24)


We get rid of parentheses

-1x^2-x^2+5x+2x-2x-10+24=0

We add all the numbers together, and all the variables

-2x^2+5x+14=0

a = -2; b = 5; c = +14;
Δ = b2-4ac
Δ = 52-4·(-2)·14
Δ = 137
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{137}}{2*-2}=\frac{-5-\sqrt{137}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{137}}{2*-2}=\frac{-5+\sqrt{137}}{-4}
$