1/5a-3=7a=

Solution for 1/5a-3=7a= equation:

1/5a-3=7a=

We move all terms to the left:

1/5a-3-(7a)=0


Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R


We add all the numbers together, and all the variables

-7a+1/5a-3=0

We multiply all the terms by the denominator


-7a*5a-3*5a+1=0

Wy multiply elements

-35a^2-15a+1=0

a = -35; b = -15; c = +1;
Δ = b2-4ac
Δ = -152-4·(-35)·1
Δ = 365
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{365}}{2*-35}=\frac{15-\sqrt{365}}{-70}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{365}}{2*-35}=\frac{15+\sqrt{365}}{-70}
$