X=7/8x-15

Solution for X=7/8x-15 equation:

X=7/8X-15

We move all terms to the left:

X-(7/8X-15)=0


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

X∈R


We get rid of parentheses

X-7/8X+15=0

We multiply all the terms by the denominator


X*8X+15*8X-7=0

Wy multiply elements

8X^2+120X-7=0

a = 8; b = 120; c = -7;
Δ = b2-4ac
Δ = 1202-4·8·(-7)
Δ = 14624
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:

$\sqrt{\Delta}=\sqrt{14624}=\sqrt{16*914}=\sqrt{16}*\sqrt{914}=4\sqrt{914}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-4\sqrt{914}}{2*8}=\frac{-120-4\sqrt{914}}{16}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+4\sqrt{914}}{2*8}=\frac{-120+4\sqrt{914}}{16}
$