(1/2)(4x+6)=15

Solution for (1/2)(4x+6)=15 equation:

(1/2)(4x+6)=15

We move all terms to the left:

(1/2)(4x+6)-(15)=0


Domain of the equation: 2)(4x+6)!=0

x∈R


We add all the numbers together, and all the variables

(+1/2)(4x+6)-15=0

We multiply parentheses ..

(+4x^2+1/2*6)-15=0

We multiply all the terms by the denominator


(+4x^2+1-15*2*6)=0

We get rid of parentheses

4x^2+1-15*2*6=0

We add all the numbers together, and all the variables

4x^2-179=0

a = 4; b = 0; c = -179;
Δ = b2-4ac
Δ = 02-4·4·(-179)
Δ = 2864
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:

$\sqrt{\Delta}=\sqrt{2864}=\sqrt{16*179}=\sqrt{16}*\sqrt{179}=4\sqrt{179}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{179}}{2*4}=\frac{0-4\sqrt{179}}{8}
=-\frac{4\sqrt{179}}{8}
=-\frac{\sqrt{179}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{179}}{2*4}=\frac{0+4\sqrt{179}}{8}
=\frac{4\sqrt{179}}{8}
=\frac{\sqrt{179}}{2}
$