X+(7)6/5x=470

Solution for X+(7)6/5x=470 equation:

X+(7)6/5X=470

We move all terms to the left:

X+(7)6/5X-(470)=0


Domain of the equation: 5X!=0

X!=0/5

X!=0

X∈R


We multiply all the terms by the denominator


X*5X-470*5X+76=0

Wy multiply elements

5X^2-2350X+76=0

a = 5; b = -2350; c = +76;
Δ = b2-4ac
Δ = -23502-4·5·76
Δ = 5520980
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:

$\sqrt{\Delta}=\sqrt{5520980}=\sqrt{4*1380245}=\sqrt{4}*\sqrt{1380245}=2\sqrt{1380245}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2350)-2\sqrt{1380245}}{2*5}=\frac{2350-2\sqrt{1380245}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2350)+2\sqrt{1380245}}{2*5}=\frac{2350+2\sqrt{1380245}}{10}
$