15/8x+22=-x+436

Solution for 15/8x+22=-x+436 equation:

15/8x+22=-x+436

We move all terms to the left:

15/8x+22-(-x+436)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

15/8x-(-1x+436)+22=0

We get rid of parentheses

15/8x+1x-436+22=0

We multiply all the terms by the denominator


1x*8x-436*8x+22*8x+15=0

Wy multiply elements

8x^2-3488x+176x+15=0

We add all the numbers together, and all the variables

8x^2-3312x+15=0

a = 8; b = -3312; c = +15;
Δ = b2-4ac
Δ = -33122-4·8·15
Δ = 10968864
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:

$\sqrt{\Delta}=\sqrt{10968864}=\sqrt{16*685554}=\sqrt{16}*\sqrt{685554}=4\sqrt{685554}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3312)-4\sqrt{685554}}{2*8}=\frac{3312-4\sqrt{685554}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3312)+4\sqrt{685554}}{2*8}=\frac{3312+4\sqrt{685554}}{16}
$