X-37=5/8x-10

Solution for X-37=5/8x-10 equation:

X-37=5/8X-10

We move all terms to the left:

X-37-(5/8X-10)=0


Domain of the equation: 8X-10)!=0

X∈R


We get rid of parentheses

X-5/8X+10-37=0

We multiply all the terms by the denominator


X*8X+10*8X-37*8X-5=0

Wy multiply elements

8X^2+80X-296X-5=0

We add all the numbers together, and all the variables

8X^2-216X-5=0

a = 8; b = -216; c = -5;
Δ = b2-4ac
Δ = -2162-4·8·(-5)
Δ = 46816
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:

$\sqrt{\Delta}=\sqrt{46816}=\sqrt{16*2926}=\sqrt{16}*\sqrt{2926}=4\sqrt{2926}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-216)-4\sqrt{2926}}{2*8}=\frac{216-4\sqrt{2926}}{16}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-216)+4\sqrt{2926}}{2*8}=\frac{216+4\sqrt{2926}}{16}
$