(1/2)(8x+6)=35

Solution for (1/2)(8x+6)=35 equation:

(1/2)(8x+6)=35

We move all terms to the left:

(1/2)(8x+6)-(35)=0


Domain of the equation: 2)(8x+6)!=0

x∈R


We add all the numbers together, and all the variables

(+1/2)(8x+6)-35=0

We multiply parentheses ..

(+8x^2+1/2*6)-35=0

We multiply all the terms by the denominator


(+8x^2+1-35*2*6)=0

We get rid of parentheses

8x^2+1-35*2*6=0

We add all the numbers together, and all the variables

8x^2-419=0

a = 8; b = 0; c = -419;
Δ = b2-4ac
Δ = 02-4·8·(-419)
Δ = 13408
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:

$\sqrt{\Delta}=\sqrt{13408}=\sqrt{16*838}=\sqrt{16}*\sqrt{838}=4\sqrt{838}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{838}}{2*8}=\frac{0-4\sqrt{838}}{16}
=-\frac{4\sqrt{838}}{16}
=-\frac{\sqrt{838}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{838}}{2*8}=\frac{0+4\sqrt{838}}{16}
=\frac{4\sqrt{838}}{16}
=\frac{\sqrt{838}}{4}
$