3/4x+5/6x=10

Solution for 3/4x+5/6x=10 equation:

3/4x+5/6x=10

We move all terms to the left:

3/4x+5/6x-(10)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We calculate fractions


18x/24x^2+20x/24x^2-10=0

We multiply all the terms by the denominator


18x+20x-10*24x^2=0

We add all the numbers together, and all the variables

38x-10*24x^2=0

Wy multiply elements

-240x^2+38x=0

a = -240; b = 38; c = 0;
Δ = b2-4ac
Δ = 382-4·(-240)·0
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-38}{2*-240}=\frac{-76}{-480}
=19/120
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+38}{2*-240}=\frac{0}{-480}
=0
$