X-5/7x+60=2x

Solution for X-5/7x+60=2x equation:

X-5/7X+60=2X

We move all terms to the left:

X-5/7X+60-(2X)=0


Domain of the equation: 7X!=0

X!=0/7

X!=0

X∈R


We add all the numbers together, and all the variables

-1X-5/7X+60=0

We multiply all the terms by the denominator


-1X*7X+60*7X-5=0

Wy multiply elements

-7X^2+420X-5=0

a = -7; b = 420; c = -5;
Δ = b2-4ac
Δ = 4202-4·(-7)·(-5)
Δ = 176260
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:

$\sqrt{\Delta}=\sqrt{176260}=\sqrt{4*44065}=\sqrt{4}*\sqrt{44065}=2\sqrt{44065}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(420)-2\sqrt{44065}}{2*-7}=\frac{-420-2\sqrt{44065}}{-14}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(420)+2\sqrt{44065}}{2*-7}=\frac{-420+2\sqrt{44065}}{-14}
$