(4/5)(x+2)=8

Solution for (4/5)(x+2)=8 equation:

(4/5)(x+2)=8

We move all terms to the left:

(4/5)(x+2)-(8)=0


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

x∈R


We add all the numbers together, and all the variables

(+4/5)(x+2)-8=0

We multiply parentheses ..

(+4x^2+4/5*2)-8=0

We multiply all the terms by the denominator


(+4x^2+4-8*5*2)=0

We get rid of parentheses

4x^2+4-8*5*2=0

We add all the numbers together, and all the variables

4x^2-76=0

a = 4; b = 0; c = -76;
Δ = b2-4ac
Δ = 02-4·4·(-76)
Δ = 1216
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:

$\sqrt{\Delta}=\sqrt{1216}=\sqrt{64*19}=\sqrt{64}*\sqrt{19}=8\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{19}}{2*4}=\frac{0-8\sqrt{19}}{8}
=-\frac{8\sqrt{19}}{8}
=-\sqrt{19}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{19}}{2*4}=\frac{0+8\sqrt{19}}{8}
=\frac{8\sqrt{19}}{8}
=\sqrt{19}
$