X=5/7x+4

Solution for X=5/7x+4 equation:

X=5/7X+4

We move all terms to the left:

X-(5/7X+4)=0


Domain of the equation: 7X+4)!=0

X∈R


We get rid of parentheses

X-5/7X-4=0

We multiply all the terms by the denominator


X*7X-4*7X-5=0

Wy multiply elements

7X^2-28X-5=0

a = 7; b = -28; c = -5;
Δ = b2-4ac
Δ = -282-4·7·(-5)
Δ = 924
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:

$\sqrt{\Delta}=\sqrt{924}=\sqrt{4*231}=\sqrt{4}*\sqrt{231}=2\sqrt{231}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{231}}{2*7}=\frac{28-2\sqrt{231}}{14}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{231}}{2*7}=\frac{28+2\sqrt{231}}{14}
$