5x-15/7x-21=0

Solution for 5x-15/7x-21=0 equation:

5x-15/7x-21=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We multiply all the terms by the denominator


5x*7x-21*7x-15=0

Wy multiply elements

35x^2-147x-15=0

a = 35; b = -147; c = -15;
Δ = b2-4ac
Δ = -1472-4·35·(-15)
Δ = 23709
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{-(-147)-\sqrt{23709}}{2*35}=\frac{147-\sqrt{23709}}{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-147)+\sqrt{23709}}{2*35}=\frac{147+\sqrt{23709}}{70}
$