x+(3/8)X=77

Solution for x+(3/8)X=77 equation:

x+(3/8)x=77

We move all terms to the left:

x+(3/8)x-(77)=0


Domain of the equation: 8)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x+(+3/8)x-77=0

We multiply parentheses

3x^2+x-77=0

a = 3; b = 1; c = -77;
Δ = b2-4ac
Δ = 12-4·3·(-77)
Δ = 925
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:

$\sqrt{\Delta}=\sqrt{925}=\sqrt{25*37}=\sqrt{25}*\sqrt{37}=5\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5\sqrt{37}}{2*3}=\frac{-1-5\sqrt{37}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5\sqrt{37}}{2*3}=\frac{-1+5\sqrt{37}}{6}
$