X=-5/9p+94

Solution for X=-5/9p+94 equation:

X=-5/9X+94

We move all terms to the left:

X-(-5/9X+94)=0


Domain of the equation: 9X+94)!=0

X∈R


We get rid of parentheses

X+5/9X-94=0

We multiply all the terms by the denominator


X*9X-94*9X+5=0

Wy multiply elements

9X^2-846X+5=0

a = 9; b = -846; c = +5;
Δ = b2-4ac
Δ = -8462-4·9·5
Δ = 715536
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:

$\sqrt{\Delta}=\sqrt{715536}=\sqrt{144*4969}=\sqrt{144}*\sqrt{4969}=12\sqrt{4969}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-846)-12\sqrt{4969}}{2*9}=\frac{846-12\sqrt{4969}}{18}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-846)+12\sqrt{4969}}{2*9}=\frac{846+12\sqrt{4969}}{18}
$