1/4x+9=7/10x-6

Solution for 1/4x+9=7/10x-6 equation:

1/4x+9=7/10x-6

We move all terms to the left:

1/4x+9-(7/10x-6)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 10x-6)!=0

x∈R


We get rid of parentheses

1/4x-7/10x+6+9=0

We calculate fractions


10x/40x^2+(-28x)/40x^2+6+9=0

We add all the numbers together, and all the variables

10x/40x^2+(-28x)/40x^2+15=0

We multiply all the terms by the denominator


10x+(-28x)+15*40x^2=0

Wy multiply elements

600x^2+10x+(-28x)=0

We get rid of parentheses

600x^2+10x-28x=0

We add all the numbers together, and all the variables

600x^2-18x=0

a = 600; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·600·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*600}=\frac{0}{1200}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*600}=\frac{36}{1200}
=3/100
$