93/4x=7/8x-10

Solution for 93/4x=7/8x-10 equation:

93/4x=7/8x-10

We move all terms to the left:

93/4x-(7/8x-10)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x-10)!=0

x∈R


We get rid of parentheses

93/4x-7/8x+10=0

We calculate fractions


744x/32x^2+(-28x)/32x^2+10=0

We multiply all the terms by the denominator


744x+(-28x)+10*32x^2=0

Wy multiply elements

320x^2+744x+(-28x)=0

We get rid of parentheses

320x^2+744x-28x=0

We add all the numbers together, and all the variables

320x^2+716x=0

a = 320; b = 716; c = 0;
Δ = b2-4ac
Δ = 7162-4·320·0
Δ = 512656
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{512656}=716$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(716)-716}{2*320}=\frac{-1432}{640}
=-2+19/80
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(716)+716}{2*320}=\frac{0}{640}
=0
$