(1/8)(x+35)=7

Solution for (1/8)(x+35)=7 equation:

(1/8)(x+35)=7

We move all terms to the left:

(1/8)(x+35)-(7)=0


Domain of the equation: 8)(x+35)!=0

x∈R


We add all the numbers together, and all the variables

(+1/8)(x+35)-7=0

We multiply parentheses ..

(+x^2+1/8*35)-7=0

We multiply all the terms by the denominator


(+x^2+1-7*8*35)=0

We get rid of parentheses

x^2+1-7*8*35=0

We add all the numbers together, and all the variables

x^2-1959=0

a = 1; b = 0; c = -1959;
Δ = b2-4ac
Δ = 02-4·1·(-1959)
Δ = 7836
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:

$\sqrt{\Delta}=\sqrt{7836}=\sqrt{4*1959}=\sqrt{4}*\sqrt{1959}=2\sqrt{1959}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{1959}}{2*1}=\frac{0-2\sqrt{1959}}{2}
=-\frac{2\sqrt{1959}}{2}
=-\sqrt{1959}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{1959}}{2*1}=\frac{0+2\sqrt{1959}}{2}
=\frac{2\sqrt{1959}}{2}
=\sqrt{1959}
$