X=7/20y-11

Solution for X=7/20y-11 equation:

X=7/20X-11

We move all terms to the left:

X-(7/20X-11)=0


Domain of the equation: 20X-11)!=0

X∈R


We get rid of parentheses

X-7/20X+11=0

We multiply all the terms by the denominator


X*20X+11*20X-7=0

Wy multiply elements

20X^2+220X-7=0

a = 20; b = 220; c = -7;
Δ = b2-4ac
Δ = 2202-4·20·(-7)
Δ = 48960
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:

$\sqrt{\Delta}=\sqrt{48960}=\sqrt{576*85}=\sqrt{576}*\sqrt{85}=24\sqrt{85}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(220)-24\sqrt{85}}{2*20}=\frac{-220-24\sqrt{85}}{40}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(220)+24\sqrt{85}}{2*20}=\frac{-220+24\sqrt{85}}{40}
$