M(x)=-2/3x+8

Solution for M(x)=-2/3x+8 equation:

(M)=-2/3M+8

We move all terms to the left:

(M)-(-2/3M+8)=0


Domain of the equation: 3M+8)!=0

M∈R


We get rid of parentheses

M+2/3M-8=0

We multiply all the terms by the denominator


M*3M-8*3M+2=0

Wy multiply elements

3M^2-24M+2=0

a = 3; b = -24; c = +2;
Δ = b2-4ac
Δ = -242-4·3·2
Δ = 552
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$M_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$M_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{552}=\sqrt{4*138}=\sqrt{4}*\sqrt{138}=2\sqrt{138}$
$M_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{138}}{2*3}=\frac{24-2\sqrt{138}}{6}
$
$M_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{138}}{2*3}=\frac{24+2\sqrt{138}}{6}
$