5x(-1x+11)=5x-7x(x-7)

Solution for 5x(-1x+11)=5x-7x(x-7) equation:

5x(-1x+11)=5x-7x(x-7)

We move all terms to the left:

5x(-1x+11)-(5x-7x(x-7))=0

We multiply parentheses

-5x^2+55x-(5x-7x(x-7))=0


We calculate terms in parentheses: -(5x-7x(x-7)), so:

5x-7x(x-7)

We multiply parentheses

-7x^2+5x+49x

We add all the numbers together, and all the variables

-7x^2+54x

Back to the equation:

-(-7x^2+54x)


We get rid of parentheses

-5x^2+7x^2-54x+55x=0

We add all the numbers together, and all the variables

2x^2+x=0

a = 2; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·2·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*2}=\frac{-2}{4}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*2}=\frac{0}{4}
=0
$