x^2+8=153-(6x-15)

Solution for x^2+8=153-(6x-15) equation:

x^2+8=153-(6x-15)

We move all terms to the left:

x^2+8-(153-(6x-15))=0


We calculate terms in parentheses: -(153-(6x-15)), so:

153-(6x-15)

determiningTheFunctionDomain
-(6x-15)+153

We get rid of parentheses

-6x+15+153

We add all the numbers together, and all the variables

-6x+168

Back to the equation:

-(-6x+168)


We get rid of parentheses

x^2+6x-168+8=0

We add all the numbers together, and all the variables

x^2+6x-160=0

a = 1; b = 6; c = -160;
Δ = b2-4ac
Δ = 62-4·1·(-160)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-26}{2*1}=\frac{-32}{2}
=-16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+26}{2*1}=\frac{20}{2}
=10
$