1.3x(10x+30)/(5)=0.5

Solution for 1.3x(10x+30)/(5)=0.5 equation:

1.3x(10x+30)/(5)=0.5

We move all terms to the left:

1.3x(10x+30)/(5)-(0.5)=0

We add all the numbers together, and all the variables

1.3x(10x+30)/5-0.5=0

We multiply all the terms by the denominator


1.3x(10x+30)-(0.5)*5=0

We add all the numbers together, and all the variables

1.3x(10x+30)-2.5=0

We multiply parentheses

10x^2+30x-2.5=0

a = 10; b = 30; c = -2.5;
Δ = b2-4ac
Δ = 302-4·10·(-2.5)
Δ = 1000
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:

$\sqrt{\Delta}=\sqrt{1000}=\sqrt{100*10}=\sqrt{100}*\sqrt{10}=10\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-10\sqrt{10}}{2*10}=\frac{-30-10\sqrt{10}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+10\sqrt{10}}{2*10}=\frac{-30+10\sqrt{10}}{20}
$