3/4x+10+x=180

Solution for 3/4x+10+x=180 equation:

3/4x+10+x=180

We move all terms to the left:

3/4x+10+x-(180)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

x+3/4x-170=0

We multiply all the terms by the denominator


x*4x-170*4x+3=0

Wy multiply elements

4x^2-680x+3=0

a = 4; b = -680; c = +3;
Δ = b2-4ac
Δ = -6802-4·4·3
Δ = 462352
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:

$\sqrt{\Delta}=\sqrt{462352}=\sqrt{16*28897}=\sqrt{16}*\sqrt{28897}=4\sqrt{28897}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-680)-4\sqrt{28897}}{2*4}=\frac{680-4\sqrt{28897}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-680)+4\sqrt{28897}}{2*4}=\frac{680+4\sqrt{28897}}{8}
$