X+5/6x+10=43

Solution for X+5/6x+10=43 equation:

X+5/6X+10=43

We move all terms to the left:

X+5/6X+10-(43)=0


Domain of the equation: 6X!=0

X!=0/6

X!=0

X∈R


We add all the numbers together, and all the variables

X+5/6X-33=0

We multiply all the terms by the denominator


X*6X-33*6X+5=0

Wy multiply elements

6X^2-198X+5=0

a = 6; b = -198; c = +5;
Δ = b2-4ac
Δ = -1982-4·6·5
Δ = 39084
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:

$\sqrt{\Delta}=\sqrt{39084}=\sqrt{4*9771}=\sqrt{4}*\sqrt{9771}=2\sqrt{9771}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-198)-2\sqrt{9771}}{2*6}=\frac{198-2\sqrt{9771}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-198)+2\sqrt{9771}}{2*6}=\frac{198+2\sqrt{9771}}{12}
$