14=-4/5x+5x-7

Solution for 14=-4/5x+5x-7 equation:

14=-4/5x+5x-7

We move all terms to the left:

14-(-4/5x+5x-7)=0


Domain of the equation: 5x+5x-7)!=0

x∈R


We add all the numbers together, and all the variables

-(5x-4/5x-7)+14=0

We get rid of parentheses

-5x+4/5x+7+14=0

We multiply all the terms by the denominator


-5x*5x+7*5x+14*5x+4=0

Wy multiply elements

-25x^2+35x+70x+4=0

We add all the numbers together, and all the variables

-25x^2+105x+4=0

a = -25; b = 105; c = +4;
Δ = b2-4ac
Δ = 1052-4·(-25)·4
Δ = 11425
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:

$\sqrt{\Delta}=\sqrt{11425}=\sqrt{25*457}=\sqrt{25}*\sqrt{457}=5\sqrt{457}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(105)-5\sqrt{457}}{2*-25}=\frac{-105-5\sqrt{457}}{-50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(105)+5\sqrt{457}}{2*-25}=\frac{-105+5\sqrt{457}}{-50}
$