X+16=3/7*5x+16

Solution for X+16=3/7*5x+16 equation:

X+16=3/7*5X+16

We move all terms to the left:

X+16-(3/7*5X+16)=0


Domain of the equation: 7*5X+16)!=0

X∈R


We get rid of parentheses

X-3/7*5X-16+16=0

We multiply all the terms by the denominator


X*7*5X-16*7*5X+16*7*5X-3=0

Wy multiply elements

35X^2*5-560X*5+560X*5-3=0

Wy multiply elements

175X^2-2800X+2800X-3=0

We add all the numbers together, and all the variables

175X^2-3=0

a = 175; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·175·(-3)
Δ = 2100
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:

$\sqrt{\Delta}=\sqrt{2100}=\sqrt{100*21}=\sqrt{100}*\sqrt{21}=10\sqrt{21}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{21}}{2*175}=\frac{0-10\sqrt{21}}{350}
=-\frac{10\sqrt{21}}{350}
=-\frac{\sqrt{21}}{35}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{21}}{2*175}=\frac{0+10\sqrt{21}}{350}
=\frac{10\sqrt{21}}{350}
=\frac{\sqrt{21}}{35}
$