(5x+12)+(55-(5x+12)/2)=55

Solution for (5x+12)+(55-(5x+12)/2)=55 equation:

(5x+12)+(55-(5x+12)/2)=55

We move all terms to the left:

(5x+12)+(55-(5x+12)/2)-(55)=0

We get rid of parentheses

5x+(55-(5x+12)/2)+12-55=0

We multiply all the terms by the denominator


5x*2)+(55-(5x+12)+12*2)-55*2)=0

We add all the numbers together, and all the variables

5x*2)+(55-(5x+12)=0

Wy multiply elements

10x^2-(5x+12)=0

We get rid of parentheses

10x^2-5x-12=0

a = 10; b = -5; c = -12;
Δ = b2-4ac
Δ = -52-4·10·(-12)
Δ = 505
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{505}}{2*10}=\frac{5-\sqrt{505}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{505}}{2*10}=\frac{5+\sqrt{505}}{20}
$