(4/5)(x+7)=20

Solution for (4/5)(x+7)=20 equation:

(4/5)(x+7)=20

We move all terms to the left:

(4/5)(x+7)-(20)=0


Domain of the equation: 5)(x+7)!=0

x∈R


We add all the numbers together, and all the variables

(+4/5)(x+7)-20=0

We multiply parentheses ..

(+4x^2+4/5*7)-20=0

We multiply all the terms by the denominator


(+4x^2+4-20*5*7)=0

We get rid of parentheses

4x^2+4-20*5*7=0

We add all the numbers together, and all the variables

4x^2-696=0

a = 4; b = 0; c = -696;
Δ = b2-4ac
Δ = 02-4·4·(-696)
Δ = 11136
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:

$\sqrt{\Delta}=\sqrt{11136}=\sqrt{64*174}=\sqrt{64}*\sqrt{174}=8\sqrt{174}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{174}}{2*4}=\frac{0-8\sqrt{174}}{8}
=-\frac{8\sqrt{174}}{8}
=-\sqrt{174}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{174}}{2*4}=\frac{0+8\sqrt{174}}{8}
=\frac{8\sqrt{174}}{8}
=\sqrt{174}
$