400=10(x-4)(x-7)

Solution for 400=10(x-4)(x-7) equation:

400=10(x-4)(x-7)

We move all terms to the left:

400-(10(x-4)(x-7))=0

We multiply parentheses ..

-(10(+x^2-7x-4x+28))+400=0


We calculate terms in parentheses: -(10(+x^2-7x-4x+28)), so:

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

We multiply parentheses

10x^2-70x-40x+280

We add all the numbers together, and all the variables

10x^2-110x+280

Back to the equation:

-(10x^2-110x+280)


We get rid of parentheses

-10x^2+110x-280+400=0

We add all the numbers together, and all the variables

-10x^2+110x+120=0

a = -10; b = 110; c = +120;
Δ = b2-4ac
Δ = 1102-4·(-10)·120
Δ = 16900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16900}=130$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(110)-130}{2*-10}=\frac{-240}{-20}
=+12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(110)+130}{2*-10}=\frac{20}{-20}
=-1
$