4/5x-7=x-10

Solution for 4/5x-7=x-10 equation:

4/5x-7=x-10

We move all terms to the left:

4/5x-7-(x-10)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

4/5x-x+10-7=0

We multiply all the terms by the denominator


-x*5x+10*5x-7*5x+4=0

Wy multiply elements

-5x^2+50x-35x+4=0

We add all the numbers together, and all the variables

-5x^2+15x+4=0

a = -5; b = 15; c = +4;
Δ = b2-4ac
Δ = 152-4·(-5)·4
Δ = 305
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{305}}{2*-5}=\frac{-15-\sqrt{305}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{305}}{2*-5}=\frac{-15+\sqrt{305}}{-10}
$