-5(1/5x-22)=8(1/2x-15)

Solution for -5(1/5x-22)=8(1/2x-15) equation:

-5(1/5x-22)=8(1/2x-15)

We move all terms to the left:

-5(1/5x-22)-(8(1/2x-15))=0


Domain of the equation: 5x-22)!=0

x∈R



Domain of the equation: 2x-15))!=0

x∈R


We multiply parentheses

-5x-(8(1/2x-15))+110=0

We multiply all the terms by the denominator


-5x*2x+110*2x-15))-(8(1-15))=0

We add all the numbers together, and all the variables

-5x*2x+110*2x-15))-(8(-14))=0

We add all the numbers together, and all the variables

-5x*2x+110*2x=0

Wy multiply elements

-10x^2+220x=0

a = -10; b = 220; c = 0;
Δ = b2-4ac
Δ = 2202-4·(-10)·0
Δ = 48400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{48400}=220$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(220)-220}{2*-10}=\frac{-440}{-20}
=+22
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(220)+220}{2*-10}=\frac{0}{-20}
=0
$