25x-7=7/10x+11

Solution for 25x-7=7/10x+11 equation:

25x-7=7/10x+11

We move all terms to the left:

25x-7-(7/10x+11)=0


Domain of the equation: 10x+11)!=0

x∈R


We get rid of parentheses

25x-7/10x-11-7=0

We multiply all the terms by the denominator


25x*10x-11*10x-7*10x-7=0

Wy multiply elements

250x^2-110x-70x-7=0

We add all the numbers together, and all the variables

250x^2-180x-7=0

a = 250; b = -180; c = -7;
Δ = b2-4ac
Δ = -1802-4·250·(-7)
Δ = 39400
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:

$\sqrt{\Delta}=\sqrt{39400}=\sqrt{100*394}=\sqrt{100}*\sqrt{394}=10\sqrt{394}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-10\sqrt{394}}{2*250}=\frac{180-10\sqrt{394}}{500}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+10\sqrt{394}}{2*250}=\frac{180+10\sqrt{394}}{500}
$