x.5(x+3)-2(x-5)=34

Solution for x.5(x+3)-2(x-5)=34 equation:

x.5(x+3)-2(x-5)=34

We move all terms to the left:

x.5(x+3)-2(x-5)-(34)=0

We multiply parentheses

x^2+3x-2x+10-34=0

We add all the numbers together, and all the variables

x^2+x-24=0

a = 1; b = 1; c = -24;
Δ = b2-4ac
Δ = 12-4·1·(-24)
Δ = 97
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{-(1)-\sqrt{97}}{2*1}=\frac{-1-\sqrt{97}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{97}}{2*1}=\frac{-1+\sqrt{97}}{2}
$