35x+910=-1/5x-2310

Solution for 35x+910=-1/5x-2310 equation:

35x+910=-1/5x-2310

We move all terms to the left:

35x+910-(-1/5x-2310)=0


Domain of the equation: 5x-2310)!=0

x∈R


We get rid of parentheses

35x+1/5x+2310+910=0

We multiply all the terms by the denominator


35x*5x+2310*5x+910*5x+1=0

Wy multiply elements

175x^2+11550x+4550x+1=0

We add all the numbers together, and all the variables

175x^2+16100x+1=0

a = 175; b = 16100; c = +1;
Δ = b2-4ac
Δ = 161002-4·175·1
Δ = 259209300
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:

$\sqrt{\Delta}=\sqrt{259209300}=\sqrt{100*2592093}=\sqrt{100}*\sqrt{2592093}=10\sqrt{2592093}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16100)-10\sqrt{2592093}}{2*175}=\frac{-16100-10\sqrt{2592093}}{350}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16100)+10\sqrt{2592093}}{2*175}=\frac{-16100+10\sqrt{2592093}}{350}
$