14a^-10/7a^-8=

Solution for 14a^-10/7a^-8= equation:

14a^-10/7a^-8=

We move all terms to the left:

14a^-10/7a^-8-()=0


Domain of the equation: 7a^!=0

a!=0/7

a!=0

a∈R


We add all the numbers together, and all the variables

14a-10/7a^=0

We multiply all the terms by the denominator


14a*7a^-10=0

Wy multiply elements

98a^2-10=0

a = 98; b = 0; c = -10;
Δ = b2-4ac
Δ = 02-4·98·(-10)
Δ = 3920
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3920}=\sqrt{784*5}=\sqrt{784}*\sqrt{5}=28\sqrt{5}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28\sqrt{5}}{2*98}=\frac{0-28\sqrt{5}}{196}
=-\frac{28\sqrt{5}}{196}
=-\frac{\sqrt{5}}{7}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28\sqrt{5}}{2*98}=\frac{0+28\sqrt{5}}{196}
=\frac{28\sqrt{5}}{196}
=\frac{\sqrt{5}}{7}
$