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 get rid of parentheses

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


We calculate terms in parentheses: -(5X(X-21)), so:

5X(X-21)

We multiply parentheses

5X^2-105X

Back to the equation:

-(5X^2-105X)


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-5X^2+102X+7=0

a = -5; b = 102; c = +7;
Δ = b2-4ac
Δ = 1022-4·(-5)·7
Δ = 10544
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:

$\sqrt{\Delta}=\sqrt{10544}=\sqrt{16*659}=\sqrt{16}*\sqrt{659}=4\sqrt{659}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(102)-4\sqrt{659}}{2*-5}=\frac{-102-4\sqrt{659}}{-10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(102)+4\sqrt{659}}{2*-5}=\frac{-102+4\sqrt{659}}{-10}
$