4/7*a-5=1

Solution for 4/7*a-5=1 equation:

4/7*a-5=1

We move all terms to the left:

4/7*a-5-(1)=0


Domain of the equation: 7*a!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

4/7*a-6=0

We multiply all the terms by the denominator


-6*7*a+4=0

Wy multiply elements

-42a*a+4=0

Wy multiply elements

-42a^2+4=0

a = -42; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-42)·4
Δ = 672
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:

$\sqrt{\Delta}=\sqrt{672}=\sqrt{16*42}=\sqrt{16}*\sqrt{42}=4\sqrt{42}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{42}}{2*-42}=\frac{0-4\sqrt{42}}{-84}
=-\frac{4\sqrt{42}}{-84}
=-\frac{\sqrt{42}}{-21}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{42}}{2*-42}=\frac{0+4\sqrt{42}}{-84}
=\frac{4\sqrt{42}}{-84}
=\frac{\sqrt{42}}{-21}
$