1x-15/7x=30

Solution for 1x-15/7x=30 equation:

1x-15/7x=30

We move all terms to the left:

1x-15/7x-(30)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

x-15/7x-30=0

We multiply all the terms by the denominator


x*7x-30*7x-15=0

Wy multiply elements

7x^2-210x-15=0

a = 7; b = -210; c = -15;
Δ = b2-4ac
Δ = -2102-4·7·(-15)
Δ = 44520
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:

$\sqrt{\Delta}=\sqrt{44520}=\sqrt{4*11130}=\sqrt{4}*\sqrt{11130}=2\sqrt{11130}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-210)-2\sqrt{11130}}{2*7}=\frac{210-2\sqrt{11130}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-210)+2\sqrt{11130}}{2*7}=\frac{210+2\sqrt{11130}}{14}
$