((1)/(2)x+15)+(3x+4)=180

Solution for ((1)/(2)x+15)+(3x+4)=180 equation:

((1)/(2)x+15)+(3x+4)=180

We move all terms to the left:

((1)/(2)x+15)+(3x+4)-(180)=0


Domain of the equation: 2x+15)!=0

x∈R


We get rid of parentheses

1/2x+3x+15+4-180=0

We multiply all the terms by the denominator


3x*2x+15*2x+4*2x-180*2x+1=0

Wy multiply elements

6x^2+30x+8x-360x+1=0

We add all the numbers together, and all the variables

6x^2-322x+1=0

a = 6; b = -322; c = +1;
Δ = b2-4ac
Δ = -3222-4·6·1
Δ = 103660
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:

$\sqrt{\Delta}=\sqrt{103660}=\sqrt{4*25915}=\sqrt{4}*\sqrt{25915}=2\sqrt{25915}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-322)-2\sqrt{25915}}{2*6}=\frac{322-2\sqrt{25915}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-322)+2\sqrt{25915}}{2*6}=\frac{322+2\sqrt{25915}}{12}
$