(1/4)(5x+7)=2x

Solution for (1/4)(5x+7)=2x equation:

(1/4)(5x+7)=2x

We move all terms to the left:

(1/4)(5x+7)-(2x)=0


Domain of the equation: 4)(5x+7)!=0

x∈R


We add all the numbers together, and all the variables

(+1/4)(5x+7)-2x=0

We add all the numbers together, and all the variables

-2x+(+1/4)(5x+7)=0

We multiply parentheses ..

(+5x^2+1/4*7)-2x=0

We multiply all the terms by the denominator


(+5x^2+1-2x*4*7)=0

We get rid of parentheses

5x^2-2x*4*7+1=0

Wy multiply elements

5x^2-56x*7+1=0

Wy multiply elements

5x^2-392x+1=0

a = 5; b = -392; c = +1;
Δ = b2-4ac
Δ = -3922-4·5·1
Δ = 153644
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:

$\sqrt{\Delta}=\sqrt{153644}=\sqrt{4*38411}=\sqrt{4}*\sqrt{38411}=2\sqrt{38411}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-392)-2\sqrt{38411}}{2*5}=\frac{392-2\sqrt{38411}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-392)+2\sqrt{38411}}{2*5}=\frac{392+2\sqrt{38411}}{10}
$