4x+3/4x+10=100-44

Solution for 4x+3/4x+10=100-44 equation:

4x+3/4x+10=100-44

We move all terms to the left:

4x+3/4x+10-(100-44)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

4x+3/4x+10-56=0

We add all the numbers together, and all the variables

4x+3/4x-46=0

We multiply all the terms by the denominator


4x*4x-46*4x+3=0

Wy multiply elements

16x^2-184x+3=0

a = 16; b = -184; c = +3;
Δ = b2-4ac
Δ = -1842-4·16·3
Δ = 33664
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:

$\sqrt{\Delta}=\sqrt{33664}=\sqrt{64*526}=\sqrt{64}*\sqrt{526}=8\sqrt{526}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-184)-8\sqrt{526}}{2*16}=\frac{184-8\sqrt{526}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-184)+8\sqrt{526}}{2*16}=\frac{184+8\sqrt{526}}{32}
$