(5/10)*(x+40)=30

Solution for (5/10)*(x+40)=30 equation:

(5/10)(x+40)=30

We move all terms to the left:

(5/10)(x+40)-(30)=0


Domain of the equation: 10)(x+40)!=0

x∈R


We add all the numbers together, and all the variables

(+5/10)(x+40)-30=0

We multiply parentheses ..

(+5x^2+5/10*40)-30=0

We multiply all the terms by the denominator


(+5x^2+5-30*10*40)=0

We get rid of parentheses

5x^2+5-30*10*40=0

We add all the numbers together, and all the variables

5x^2-11995=0

a = 5; b = 0; c = -11995;
Δ = b2-4ac
Δ = 02-4·5·(-11995)
Δ = 239900
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:

$\sqrt{\Delta}=\sqrt{239900}=\sqrt{100*2399}=\sqrt{100}*\sqrt{2399}=10\sqrt{2399}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{2399}}{2*5}=\frac{0-10\sqrt{2399}}{10}
=-\frac{10\sqrt{2399}}{10}
=-\sqrt{2399}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{2399}}{2*5}=\frac{0+10\sqrt{2399}}{10}
=\frac{10\sqrt{2399}}{10}
=\sqrt{2399}
$