X=(1p2+12p)-(6p2-22p)

Solution for X=(1p2+12p)-(6p2-22p) equation:

X=(1X^2+12X)-(6X^2-22X)

We move all terms to the left:

X-((1X^2+12X)-(6X^2-22X))=0


We calculate terms in parentheses: -((1X^2+12X)-(6X^2-22X)), so:

(1X^2+12X)-(6X^2-22X)

We get rid of parentheses

1X^2-6X^2+12X+22X

We add all the numbers together, and all the variables

-5X^2+34X

Back to the equation:

-(-5X^2+34X)


We get rid of parentheses

5X^2-34X+X=0

We add all the numbers together, and all the variables

5X^2-33X=0

a = 5; b = -33; c = 0;
Δ = b2-4ac
Δ = -332-4·5·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-33}{2*5}=\frac{0}{10}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+33}{2*5}=\frac{66}{10}
=6+3/5
$