X=76-65-97/4*2x

Solution for X=76-65-97/4*2x equation:

X=76-65-97/4*2X

We move all terms to the left:

X-(76-65-97/4*2X)=0


Domain of the equation: 4*2X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(-97/4*2X+11)=0

We get rid of parentheses

X+97/4*2X-11=0

We multiply all the terms by the denominator


X*4*2X-11*4*2X+97=0

Wy multiply elements

8X^2*2-88X*2+97=0

Wy multiply elements

16X^2-176X+97=0

a = 16; b = -176; c = +97;
Δ = b2-4ac
Δ = -1762-4·16·97
Δ = 24768
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:

$\sqrt{\Delta}=\sqrt{24768}=\sqrt{576*43}=\sqrt{576}*\sqrt{43}=24\sqrt{43}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-176)-24\sqrt{43}}{2*16}=\frac{176-24\sqrt{43}}{32}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-176)+24\sqrt{43}}{2*16}=\frac{176+24\sqrt{43}}{32}
$