X=34+(3x-68)/2

Solution for X=34+(3x-68)/2 equation:

X=34+(3X-68)/2

We move all terms to the left:

X-(34+(3X-68)/2)=0

We multiply all the terms by the denominator


X*2)-(34+(3X-68)=0

Wy multiply elements

2X^2+(3X-68)=0

We get rid of parentheses

2X^2+3X-68=0

a = 2; b = 3; c = -68;
Δ = b2-4ac
Δ = 32-4·2·(-68)
Δ = 553
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{-(3)-\sqrt{553}}{2*2}=\frac{-3-\sqrt{553}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{553}}{2*2}=\frac{-3+\sqrt{553}}{4}
$