5(1/2)+1(3/10)x=13

Solution for 5(1/2)+1(3/10)x=13 equation:

5(1/2)+1(3/10)x=13

We move all terms to the left:

5(1/2)+1(3/10)x-(13)=0


Domain of the equation: 10)x!=0

x!=0/1

x!=0

x∈R


determiningTheFunctionDomain
1(3/10)x-13+5(1/2)=0

We add all the numbers together, and all the variables

1(+3/10)x-13+5(+1/2)=0

We multiply parentheses

3x^2-13+1/2*5=0

We multiply all the terms by the denominator


3x^2*2*5+1-13*2*5=0

We add all the numbers together, and all the variables

3x^2*2*5-129=0

Wy multiply elements

30x^2*5-129=0

Wy multiply elements

150x^2-129=0

a = 150; b = 0; c = -129;
Δ = b2-4ac
Δ = 02-4·150·(-129)
Δ = 77400
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:

$\sqrt{\Delta}=\sqrt{77400}=\sqrt{900*86}=\sqrt{900}*\sqrt{86}=30\sqrt{86}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{86}}{2*150}=\frac{0-30\sqrt{86}}{300}
=-\frac{30\sqrt{86}}{300}
=-\frac{\sqrt{86}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{86}}{2*150}=\frac{0+30\sqrt{86}}{300}
=\frac{30\sqrt{86}}{300}
=\frac{\sqrt{86}}{10}
$