(x)=-4/5x+6

Solution for (x)=-4/5x+6 equation:

(x)=-4/5x+6

We move all terms to the left:

(x)-(-4/5x+6)=0


Domain of the equation: 5x+6)!=0

x∈R


We get rid of parentheses

x+4/5x-6=0

We multiply all the terms by the denominator


x*5x-6*5x+4=0

Wy multiply elements

5x^2-30x+4=0

a = 5; b = -30; c = +4;
Δ = b2-4ac
Δ = -302-4·5·4
Δ = 820
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:

$\sqrt{\Delta}=\sqrt{820}=\sqrt{4*205}=\sqrt{4}*\sqrt{205}=2\sqrt{205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{205}}{2*5}=\frac{30-2\sqrt{205}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{205}}{2*5}=\frac{30+2\sqrt{205}}{10}
$