x^2-5x=7(5-x)

Solution for x^2-5x=7(5-x) equation:

x^2-5x=7(5-x)

We move all terms to the left:

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

We add all the numbers together, and all the variables

x^2-5x-(7(-1x+5))=0


We calculate terms in parentheses: -(7(-1x+5)), so:

7(-1x+5)

We multiply parentheses

-7x+35

Back to the equation:

-(-7x+35)


We get rid of parentheses

x^2-5x+7x-35=0

We add all the numbers together, and all the variables

x^2+2x-35=0

a = 1; b = 2; c = -35;
Δ = b2-4ac
Δ = 22-4·1·(-35)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-12}{2*1}=\frac{-14}{2}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+12}{2*1}=\frac{10}{2}
=5
$