5x+7=2/5x+30

Solution for 5x+7=2/5x+30 equation:

5x+7=2/5x+30

We move all terms to the left:

5x+7-(2/5x+30)=0


Domain of the equation: 5x+30)!=0

x∈R


We get rid of parentheses

5x-2/5x-30+7=0

We multiply all the terms by the denominator


5x*5x-30*5x+7*5x-2=0

Wy multiply elements

25x^2-150x+35x-2=0

We add all the numbers together, and all the variables

25x^2-115x-2=0

a = 25; b = -115; c = -2;
Δ = b2-4ac
Δ = -1152-4·25·(-2)
Δ = 13425
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:

$\sqrt{\Delta}=\sqrt{13425}=\sqrt{25*537}=\sqrt{25}*\sqrt{537}=5\sqrt{537}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-115)-5\sqrt{537}}{2*25}=\frac{115-5\sqrt{537}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-115)+5\sqrt{537}}{2*25}=\frac{115+5\sqrt{537}}{50}
$