5X(5x-3)=6X(4x+1)

Solution for 5X(5x-3)=6X(4x+1) equation:

5X(5X-3)=6X(4X+1)

We move all terms to the left:

5X(5X-3)-(6X(4X+1))=0

We multiply parentheses

25X^2-15X-(6X(4X+1))=0


We calculate terms in parentheses: -(6X(4X+1)), so:

6X(4X+1)

We multiply parentheses

24X^2+6X

Back to the equation:

-(24X^2+6X)


We get rid of parentheses

25X^2-24X^2-15X-6X=0

We add all the numbers together, and all the variables

X^2-21X=0

a = 1; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·1·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*1}=\frac{0}{2}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*1}=\frac{42}{2}
=21
$