3/4x=2x-25

Solution for 3/4x=2x-25 equation:

3/4x=2x-25

We move all terms to the left:

3/4x-(2x-25)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x-2x+25=0

We multiply all the terms by the denominator


-2x*4x+25*4x+3=0

Wy multiply elements

-8x^2+100x+3=0

a = -8; b = 100; c = +3;
Δ = b2-4ac
Δ = 1002-4·(-8)·3
Δ = 10096
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:

$\sqrt{\Delta}=\sqrt{10096}=\sqrt{16*631}=\sqrt{16}*\sqrt{631}=4\sqrt{631}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-4\sqrt{631}}{2*-8}=\frac{-100-4\sqrt{631}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+4\sqrt{631}}{2*-8}=\frac{-100+4\sqrt{631}}{-16}
$