x+3/4x=10

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

X+3/4X=10

We move all terms to the left:

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


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We multiply all the terms by the denominator


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

Wy multiply elements

4X^2-40X+3=0

a = 4; b = -40; c = +3;
Δ = b2-4ac
Δ = -402-4·4·3
Δ = 1552
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:

$\sqrt{\Delta}=\sqrt{1552}=\sqrt{16*97}=\sqrt{16}*\sqrt{97}=4\sqrt{97}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{97}}{2*4}=\frac{40-4\sqrt{97}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{97}}{2*4}=\frac{40+4\sqrt{97}}{8}
$