-4/5x-3/20x+1/4=-70

Solution for -4/5x-3/20x+1/4=-70 equation:

-4/5x-3/20x+1/4=-70

We move all terms to the left:

-4/5x-3/20x+1/4-(-70)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 20x!=0

x!=0/20

x!=0

x∈R


We add all the numbers together, and all the variables

-4/5x-3/20x+70+1/4=0

We calculate fractions


200x^2/1600x^2+(-1280x)/1600x^2+(-240x)/1600x^2+70=0

We multiply all the terms by the denominator


200x^2+(-1280x)+(-240x)+70*1600x^2=0

Wy multiply elements

200x^2+112000x^2+(-1280x)+(-240x)=0

We get rid of parentheses

200x^2+112000x^2-1280x-240x=0

We add all the numbers together, and all the variables

112200x^2-1520x=0

a = 112200; b = -1520; c = 0;
Δ = b2-4ac
Δ = -15202-4·112200·0
Δ = 2310400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2310400}=1520$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1520)-1520}{2*112200}=\frac{0}{224400}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1520)+1520}{2*112200}=\frac{3040}{224400}
=38/2805
$