4(10)=(x-7)(-4+x)

Solution for 4(10)=(x-7)(-4+x) equation:

4(10)=(x-7)(-4+x)

We move all terms to the left:

4(10)-((x-7)(-4+x))=0

We add all the numbers together, and all the variables

-((x-7)(x-4))+410=0

We multiply parentheses ..

-((+x^2-4x-7x+28))+410=0


We calculate terms in parentheses: -((+x^2-4x-7x+28)), so:

(+x^2-4x-7x+28)

We get rid of parentheses

x^2-4x-7x+28

We add all the numbers together, and all the variables

x^2-11x+28

Back to the equation:

-(x^2-11x+28)


We get rid of parentheses

-x^2+11x-28+410=0

We add all the numbers together, and all the variables

-1x^2+11x+382=0

a = -1; b = 11; c = +382;
Δ = b2-4ac
Δ = 112-4·(-1)·382
Δ = 1649
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{1649}}{2*-1}=\frac{-11-\sqrt{1649}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{1649}}{2*-1}=\frac{-11+\sqrt{1649}}{-2}
$