X+3/5y=56

Solution for X+3/5y=56 equation:

X+3/5X=56

We move all terms to the left:

X+3/5X-(56)=0


Domain of the equation: 5X!=0

X!=0/5

X!=0

X∈R


We multiply all the terms by the denominator


X*5X-56*5X+3=0

Wy multiply elements

5X^2-280X+3=0

a = 5; b = -280; c = +3;
Δ = b2-4ac
Δ = -2802-4·5·3
Δ = 78340
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:

$\sqrt{\Delta}=\sqrt{78340}=\sqrt{4*19585}=\sqrt{4}*\sqrt{19585}=2\sqrt{19585}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-280)-2\sqrt{19585}}{2*5}=\frac{280-2\sqrt{19585}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-280)+2\sqrt{19585}}{2*5}=\frac{280+2\sqrt{19585}}{10}
$