x-(4x-7)=5x-(x+21)4x

Solution for x-(4x-7)=5x-(x+21)4x equation:

x-(4x-7)=5x-(x+21)4x

We move all terms to the left:

x-(4x-7)-(5x-(x+21)4x)=0

We get rid of parentheses

x-4x-(5x-(x+21)4x)+7=0


We calculate terms in parentheses: -(5x-(x+21)4x), so:

5x-(x+21)4x

We multiply parentheses

-4x^2+5x-84x

We add all the numbers together, and all the variables

-4x^2-79x

Back to the equation:

-(-4x^2-79x)


We add all the numbers together, and all the variables

-(-4x^2-79x)-3x+7=0

We get rid of parentheses

4x^2+79x-3x+7=0

We add all the numbers together, and all the variables

4x^2+76x+7=0

a = 4; b = 76; c = +7;
Δ = b2-4ac
Δ = 762-4·4·7
Δ = 5664
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:

$\sqrt{\Delta}=\sqrt{5664}=\sqrt{16*354}=\sqrt{16}*\sqrt{354}=4\sqrt{354}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(76)-4\sqrt{354}}{2*4}=\frac{-76-4\sqrt{354}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(76)+4\sqrt{354}}{2*4}=\frac{-76+4\sqrt{354}}{8}
$