70=10x-1/4x

Solution for 70=10x-1/4x equation:

70=10x-1/4x

We move all terms to the left:

70-(10x-1/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+10x-1/4x)+70=0

We get rid of parentheses

-10x+1/4x+70=0

We multiply all the terms by the denominator


-10x*4x+70*4x+1=0

Wy multiply elements

-40x^2+280x+1=0

a = -40; b = 280; c = +1;
Δ = b2-4ac
Δ = 2802-4·(-40)·1
Δ = 78560
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:

$\sqrt{\Delta}=\sqrt{78560}=\sqrt{16*4910}=\sqrt{16}*\sqrt{4910}=4\sqrt{4910}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(280)-4\sqrt{4910}}{2*-40}=\frac{-280-4\sqrt{4910}}{-80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(280)+4\sqrt{4910}}{2*-40}=\frac{-280+4\sqrt{4910}}{-80}
$