4/5x+6=2X-22

Solution for 4/5x+6=2X-22 equation:

4/5x+6=2x-22

We move all terms to the left:

4/5x+6-(2x-22)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

4/5x-2x+22+6=0

We multiply all the terms by the denominator


-2x*5x+22*5x+6*5x+4=0

Wy multiply elements

-10x^2+110x+30x+4=0

We add all the numbers together, and all the variables

-10x^2+140x+4=0

a = -10; b = 140; c = +4;
Δ = b2-4ac
Δ = 1402-4·(-10)·4
Δ = 19760
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:

$\sqrt{\Delta}=\sqrt{19760}=\sqrt{16*1235}=\sqrt{16}*\sqrt{1235}=4\sqrt{1235}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(140)-4\sqrt{1235}}{2*-10}=\frac{-140-4\sqrt{1235}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(140)+4\sqrt{1235}}{2*-10}=\frac{-140+4\sqrt{1235}}{-20}
$