36-7x=7x(x-5)

Solution for 36-7x=7x(x-5) equation:

36-7x=7x(x-5)

We move all terms to the left:

36-7x-(7x(x-5))=0


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

7x(x-5)

We multiply parentheses

7x^2-35x

Back to the equation:

-(7x^2-35x)


We get rid of parentheses

-7x^2-7x+35x+36=0

We add all the numbers together, and all the variables

-7x^2+28x+36=0

a = -7; b = 28; c = +36;
Δ = b2-4ac
Δ = 282-4·(-7)·36
Δ = 1792
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1792}=\sqrt{256*7}=\sqrt{256}*\sqrt{7}=16\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-16\sqrt{7}}{2*-7}=\frac{-28-16\sqrt{7}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+16\sqrt{7}}{2*-7}=\frac{-28+16\sqrt{7}}{-14}
$