4/5x+60=x+7

Solution for 4/5x+60=x+7 equation:

4/5x+60=x+7

We move all terms to the left:

4/5x+60-(x+7)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

4/5x-x-7+60=0

We multiply all the terms by the denominator


-x*5x-7*5x+60*5x+4=0

Wy multiply elements

-5x^2-35x+300x+4=0

We add all the numbers together, and all the variables

-5x^2+265x+4=0

a = -5; b = 265; c = +4;
Δ = b2-4ac
Δ = 2652-4·(-5)·4
Δ = 70305
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{-(265)-\sqrt{70305}}{2*-5}=\frac{-265-\sqrt{70305}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(265)+\sqrt{70305}}{2*-5}=\frac{-265+\sqrt{70305}}{-10}
$