(1/2)(5x+10)=6

Solution for (1/2)(5x+10)=6 equation:

(1/2)(5x+10)=6

We move all terms to the left:

(1/2)(5x+10)-(6)=0


Domain of the equation: 2)(5x+10)!=0

x∈R


We add all the numbers together, and all the variables

(+1/2)(5x+10)-6=0

We multiply parentheses ..

(+5x^2+1/2*10)-6=0

We multiply all the terms by the denominator


(+5x^2+1-6*2*10)=0

We get rid of parentheses

5x^2+1-6*2*10=0

We add all the numbers together, and all the variables

5x^2-119=0

a = 5; b = 0; c = -119;
Δ = b2-4ac
Δ = 02-4·5·(-119)
Δ = 2380
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:

$\sqrt{\Delta}=\sqrt{2380}=\sqrt{4*595}=\sqrt{4}*\sqrt{595}=2\sqrt{595}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{595}}{2*5}=\frac{0-2\sqrt{595}}{10}
=-\frac{2\sqrt{595}}{10}
=-\frac{\sqrt{595}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{595}}{2*5}=\frac{0+2\sqrt{595}}{10}
=\frac{2\sqrt{595}}{10}
=\frac{\sqrt{595}}{5}
$