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

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

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

We move all terms to the left:

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


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

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We multiply all the terms by the denominator


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

We get rid of parentheses

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

We add all the numbers together, and all the variables

5x^2-59=0

a = 5; b = 0; c = -59;
Δ = b2-4ac
Δ = 02-4·5·(-59)
Δ = 1180
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:

$\sqrt{\Delta}=\sqrt{1180}=\sqrt{4*295}=\sqrt{4}*\sqrt{295}=2\sqrt{295}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{295}}{2*5}=\frac{0-2\sqrt{295}}{10}
=-\frac{2\sqrt{295}}{10}
=-\frac{\sqrt{295}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{295}}{2*5}=\frac{0+2\sqrt{295}}{10}
=\frac{2\sqrt{295}}{10}
=\frac{\sqrt{295}}{5}
$