(2/5)x+7/15=157/15

Solution for (2/5)x+7/15=157/15 equation:

(2/5)x+7/15=157/15

We move all terms to the left:

(2/5)x+7/15-(157/15)=0


Domain of the equation: 5)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+2/5)x+7/15-(+157/15)=0

We multiply parentheses

2x^2+7/15-(+157/15)=0

We get rid of parentheses

2x^2+7/15-157/15=0

We multiply all the terms by the denominator


2x^2*15+7-157=0

We add all the numbers together, and all the variables

2x^2*15-150=0

Wy multiply elements

30x^2-150=0

a = 30; b = 0; c = -150;
Δ = b2-4ac
Δ = 02-4·30·(-150)
Δ = 18000
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:

$\sqrt{\Delta}=\sqrt{18000}=\sqrt{3600*5}=\sqrt{3600}*\sqrt{5}=60\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60\sqrt{5}}{2*30}=\frac{0-60\sqrt{5}}{60}
=-\frac{60\sqrt{5}}{60}
=-\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60\sqrt{5}}{2*30}=\frac{0+60\sqrt{5}}{60}
=\frac{60\sqrt{5}}{60}
=\sqrt{5}
$