(X-6)(x-6)=10x+(X-4)

Solution for (X-6)(x-6)=10x+(X-4) equation:

(X-6)(X-6)=10X+(X-4)

We move all terms to the left:

(X-6)(X-6)-(10X+(X-4))=0

We multiply parentheses ..

(+X^2-6X-6X+36)-(10X+(X-4))=0


We calculate terms in parentheses: -(10X+(X-4)), so:

10X+(X-4)

We get rid of parentheses

10X+X-4

We add all the numbers together, and all the variables

11X-4

Back to the equation:

-(11X-4)


We get rid of parentheses

X^2-6X-6X-11X+36+4=0

We add all the numbers together, and all the variables

X^2-23X+40=0

a = 1; b = -23; c = +40;
Δ = b2-4ac
Δ = -232-4·1·40
Δ = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-3\sqrt{41}}{2*1}=\frac{23-3\sqrt{41}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+3\sqrt{41}}{2*1}=\frac{23+3\sqrt{41}}{2}
$