(7-5x)7=11x(-3x+5)

Solution for (7-5x)7=11x(-3x+5) equation:

(7-5x)7=11x(-3x+5)

We move all terms to the left:

(7-5x)7-(11x(-3x+5))=0

We add all the numbers together, and all the variables

(-5x+7)7-(11x(-3x+5))=0

We multiply parentheses

-35x-(11x(-3x+5))+49=0


We calculate terms in parentheses: -(11x(-3x+5)), so:

11x(-3x+5)

We multiply parentheses

-33x^2+55x

Back to the equation:

-(-33x^2+55x)


We get rid of parentheses

33x^2-55x-35x+49=0

We add all the numbers together, and all the variables

33x^2-90x+49=0

a = 33; b = -90; c = +49;
Δ = b2-4ac
Δ = -902-4·33·49
Δ = 1632
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:

$\sqrt{\Delta}=\sqrt{1632}=\sqrt{16*102}=\sqrt{16}*\sqrt{102}=4\sqrt{102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-4\sqrt{102}}{2*33}=\frac{90-4\sqrt{102}}{66}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+4\sqrt{102}}{2*33}=\frac{90+4\sqrt{102}}{66}
$