(1/4)(5x+3)=2x

Solution for (1/4)(5x+3)=2x equation:

(1/4)(5x+3)=2x

We move all terms to the left:

(1/4)(5x+3)-(2x)=0


Domain of the equation: 4)(5x+3)!=0

x∈R


We add all the numbers together, and all the variables

(+1/4)(5x+3)-2x=0

We add all the numbers together, and all the variables

-2x+(+1/4)(5x+3)=0

We multiply parentheses ..

(+5x^2+1/4*3)-2x=0

We multiply all the terms by the denominator


(+5x^2+1-2x*4*3)=0

We get rid of parentheses

5x^2-2x*4*3+1=0

Wy multiply elements

5x^2-24x*3+1=0

Wy multiply elements

5x^2-72x+1=0

a = 5; b = -72; c = +1;
Δ = b2-4ac
Δ = -722-4·5·1
Δ = 5164
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:

$\sqrt{\Delta}=\sqrt{5164}=\sqrt{4*1291}=\sqrt{4}*\sqrt{1291}=2\sqrt{1291}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-2\sqrt{1291}}{2*5}=\frac{72-2\sqrt{1291}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+2\sqrt{1291}}{2*5}=\frac{72+2\sqrt{1291}}{10}
$