X=(1/2)(15-8y)

Solution for X=(1/2)(15-8y) equation:

X=(1/2)(15-8X)

We move all terms to the left:

X-((1/2)(15-8X))=0


Domain of the equation: 2)(15-8X))!=0

X∈R


We add all the numbers together, and all the variables

X-((+1/2)(-8X+15))=0

We multiply parentheses ..

-((-8X^2+1/2*15))+X=0

We multiply all the terms by the denominator


-((-8X^2+1+X*2*15))=0


We calculate terms in parentheses: -((-8X^2+1+X*2*15)), so:

(-8X^2+1+X*2*15)

We get rid of parentheses

-8X^2+X*2*15+1

Wy multiply elements

-8X^2+30X*1+1

Wy multiply elements

-8X^2+30X+1

Back to the equation:

-(-8X^2+30X+1)


We get rid of parentheses

8X^2-30X-1=0

a = 8; b = -30; c = -1;
Δ = b2-4ac
Δ = -302-4·8·(-1)
Δ = 932
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:

$\sqrt{\Delta}=\sqrt{932}=\sqrt{4*233}=\sqrt{4}*\sqrt{233}=2\sqrt{233}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{233}}{2*8}=\frac{30-2\sqrt{233}}{16}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{233}}{2*8}=\frac{30+2\sqrt{233}}{16}
$