-1x+60=8/5x+72

Solution for -1x+60=8/5x+72 equation:

-1x+60=8/5x+72

We move all terms to the left:

-1x+60-(8/5x+72)=0


Domain of the equation: 5x+72)!=0

x∈R


We get rid of parentheses

-1x-8/5x-72+60=0

We multiply all the terms by the denominator


-1x*5x-72*5x+60*5x-8=0

Wy multiply elements

-5x^2-360x+300x-8=0

We add all the numbers together, and all the variables

-5x^2-60x-8=0

a = -5; b = -60; c = -8;
Δ = b2-4ac
Δ = -602-4·(-5)·(-8)
Δ = 3440
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:

$\sqrt{\Delta}=\sqrt{3440}=\sqrt{16*215}=\sqrt{16}*\sqrt{215}=4\sqrt{215}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{215}}{2*-5}=\frac{60-4\sqrt{215}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{215}}{2*-5}=\frac{60+4\sqrt{215}}{-10}
$