2x^2+10x=52/105

Solution for 2x^2+10x=52/105 equation:

2x^2+10x=52/105

We move all terms to the left:

2x^2+10x-(52/105)=0

We add all the numbers together, and all the variables

2x^2+10x-(+52/105)=0

We get rid of parentheses

2x^2+10x-52/105=0

We multiply all the terms by the denominator


2x^2*105+10x*105-52=0

Wy multiply elements

210x^2+1050x-52=0

a = 210; b = 1050; c = -52;
Δ = b2-4ac
Δ = 10502-4·210·(-52)
Δ = 1146180
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:

$\sqrt{\Delta}=\sqrt{1146180}=\sqrt{4*286545}=\sqrt{4}*\sqrt{286545}=2\sqrt{286545}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1050)-2\sqrt{286545}}{2*210}=\frac{-1050-2\sqrt{286545}}{420}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1050)+2\sqrt{286545}}{2*210}=\frac{-1050+2\sqrt{286545}}{420}
$