X-7=2/5x+20

Solution for X-7=2/5x+20 equation:

X-7=2/5X+20

We move all terms to the left:

X-7-(2/5X+20)=0


Domain of the equation: 5X+20)!=0

X∈R


We get rid of parentheses

X-2/5X-20-7=0

We multiply all the terms by the denominator


X*5X-20*5X-7*5X-2=0

Wy multiply elements

5X^2-100X-35X-2=0

We add all the numbers together, and all the variables

5X^2-135X-2=0

a = 5; b = -135; c = -2;
Δ = b2-4ac
Δ = -1352-4·5·(-2)
Δ = 18265
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-135)-\sqrt{18265}}{2*5}=\frac{135-\sqrt{18265}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-135)+\sqrt{18265}}{2*5}=\frac{135+\sqrt{18265}}{10}
$