26=-2/5x+4x-10

Solution for 26=-2/5x+4x-10 equation:

26=-2/5x+4x-10

We move all terms to the left:

26-(-2/5x+4x-10)=0


Domain of the equation: 5x+4x-10)!=0

x∈R


We add all the numbers together, and all the variables

-(4x-2/5x-10)+26=0

We get rid of parentheses

-4x+2/5x+10+26=0

We multiply all the terms by the denominator


-4x*5x+10*5x+26*5x+2=0

Wy multiply elements

-20x^2+50x+130x+2=0

We add all the numbers together, and all the variables

-20x^2+180x+2=0

a = -20; b = 180; c = +2;
Δ = b2-4ac
Δ = 1802-4·(-20)·2
Δ = 32560
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:

$\sqrt{\Delta}=\sqrt{32560}=\sqrt{16*2035}=\sqrt{16}*\sqrt{2035}=4\sqrt{2035}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-4\sqrt{2035}}{2*-20}=\frac{-180-4\sqrt{2035}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+4\sqrt{2035}}{2*-20}=\frac{-180+4\sqrt{2035}}{-40}
$