3/4x+4x+10=90

Solution for 3/4x+4x+10=90 equation:

3/4x+4x+10=90

We move all terms to the left:

3/4x+4x+10-(90)=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-80=0

We multiply all the terms by the denominator


4x*4x-80*4x+3=0

Wy multiply elements

16x^2-320x+3=0

a = 16; b = -320; c = +3;
Δ = b2-4ac
Δ = -3202-4·16·3
Δ = 102208
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:

$\sqrt{\Delta}=\sqrt{102208}=\sqrt{64*1597}=\sqrt{64}*\sqrt{1597}=8\sqrt{1597}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-320)-8\sqrt{1597}}{2*16}=\frac{320-8\sqrt{1597}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-320)+8\sqrt{1597}}{2*16}=\frac{320+8\sqrt{1597}}{32}
$