X-4/3y=10

Solution for X-4/3y=10 equation:

X-4/3X=10

We move all terms to the left:

X-4/3X-(10)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We multiply all the terms by the denominator


X*3X-10*3X-4=0

Wy multiply elements

3X^2-30X-4=0

a = 3; b = -30; c = -4;
Δ = b2-4ac
Δ = -302-4·3·(-4)
Δ = 948
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:

$\sqrt{\Delta}=\sqrt{948}=\sqrt{4*237}=\sqrt{4}*\sqrt{237}=2\sqrt{237}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{237}}{2*3}=\frac{30-2\sqrt{237}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{237}}{2*3}=\frac{30+2\sqrt{237}}{6}
$