(X+2)x=(6x+10)

Solution for (X+2)x=(6x+10) equation:

(X+2)X=(6X+10)

We move all terms to the left:

(X+2)X-((6X+10))=0

We multiply parentheses

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


We calculate terms in parentheses: -((6X+10)), so:

(6X+10)

We get rid of parentheses

6X+10

Back to the equation:

-(6X+10)


We get rid of parentheses

X^2+2X-6X-10=0

We add all the numbers together, and all the variables

X^2-4X-10=0

a = 1; b = -4; c = -10;
Δ = b2-4ac
Δ = -42-4·1·(-10)
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{14}}{2*1}=\frac{4-2\sqrt{14}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{14}}{2*1}=\frac{4+2\sqrt{14}}{2}
$