(4x-84)+(x+24)+(1/2x+42)=180

Solution for (4x-84)+(x+24)+(1/2x+42)=180 equation:

(4x-84)+(x+24)+(1/2x+42)=180

We move all terms to the left:

(4x-84)+(x+24)+(1/2x+42)-(180)=0


Domain of the equation: 2x+42)!=0

x∈R


We get rid of parentheses

4x+x+1/2x-84+24+42-180=0

We multiply all the terms by the denominator


4x*2x+x*2x-84*2x+24*2x+42*2x-180*2x+1=0

Wy multiply elements

8x^2+2x^2-168x+48x+84x-360x+1=0

We add all the numbers together, and all the variables

10x^2-396x+1=0

a = 10; b = -396; c = +1;
Δ = b2-4ac
Δ = -3962-4·10·1
Δ = 156776
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:

$\sqrt{\Delta}=\sqrt{156776}=\sqrt{4*39194}=\sqrt{4}*\sqrt{39194}=2\sqrt{39194}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-396)-2\sqrt{39194}}{2*10}=\frac{396-2\sqrt{39194}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-396)+2\sqrt{39194}}{2*10}=\frac{396+2\sqrt{39194}}{20}
$