(x+2)*(7-3)=(x-4)*(x-3)

Solution for (x+2)*(7-3)=(x-4)*(x-3) equation:

(x+2)(7-3)=(x-4)(x-3)

We move all terms to the left:

(x+2)(7-3)-((x-4)(x-3))=0

We add all the numbers together, and all the variables

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

We multiply parentheses

4x-((x-4)(x-3))+8=0

We multiply parentheses ..

-((+x^2-3x-4x+12))+4x+8=0


We calculate terms in parentheses: -((+x^2-3x-4x+12)), so:

(+x^2-3x-4x+12)

We get rid of parentheses

x^2-3x-4x+12

We add all the numbers together, and all the variables

x^2-7x+12

Back to the equation:

-(x^2-7x+12)


We add all the numbers together, and all the variables

4x-(x^2-7x+12)+8=0

We get rid of parentheses

-x^2+4x+7x-12+8=0

We add all the numbers together, and all the variables

-1x^2+11x-4=0

a = -1; b = 11; c = -4;
Δ = b2-4ac
Δ = 112-4·(-1)·(-4)
Δ = 105
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{-(11)-\sqrt{105}}{2*-1}=\frac{-11-\sqrt{105}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{105}}{2*-1}=\frac{-11+\sqrt{105}}{-2}
$