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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

x-(4x-7)-(5x(-1x+21))=0

We get rid of parentheses

x-4x-(5x(-1x+21))+7=0


We calculate terms in parentheses: -(5x(-1x+21)), so:

5x(-1x+21)

We multiply parentheses

-5x^2+105x

Back to the equation:

-(-5x^2+105x)


We add all the numbers together, and all the variables

-(-5x^2+105x)-3x+7=0

We get rid of parentheses

5x^2-105x-3x+7=0

We add all the numbers together, and all the variables

5x^2-108x+7=0

a = 5; b = -108; c = +7;
Δ = b2-4ac
Δ = -1082-4·5·7
Δ = 11524
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:

$\sqrt{\Delta}=\sqrt{11524}=\sqrt{4*2881}=\sqrt{4}*\sqrt{2881}=2\sqrt{2881}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-2\sqrt{2881}}{2*5}=\frac{108-2\sqrt{2881}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+2\sqrt{2881}}{2*5}=\frac{108+2\sqrt{2881}}{10}
$