X(x-15)=4(x-15)4

Solution for X(x-15)=4(x-15)4 equation:

X(X-15)=4(X-15)4

We move all terms to the left:

X(X-15)-(4(X-15)4)=0

We multiply parentheses

X^2-15X-(4(X-15)4)=0


We calculate terms in parentheses: -(4(X-15)4), so:

4(X-15)4

We multiply parentheses

16X-240

Back to the equation:

-(16X-240)


We get rid of parentheses

X^2-15X-16X+240=0

We add all the numbers together, and all the variables

X^2-31X+240=0

a = 1; b = -31; c = +240;
Δ = b2-4ac
Δ = -312-4·1·240
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-1}{2*1}=\frac{30}{2}
=15
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+1}{2*1}=\frac{32}{2}
=16
$