-10x+3/4x=200

Solution for -10x+3/4x=200 equation:

-10x+3/4x=200

We move all terms to the left:

-10x+3/4x-(200)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


-10x*4x-200*4x+3=0

Wy multiply elements

-40x^2-800x+3=0

a = -40; b = -800; c = +3;
Δ = b2-4ac
Δ = -8002-4·(-40)·3
Δ = 640480
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:

$\sqrt{\Delta}=\sqrt{640480}=\sqrt{16*40030}=\sqrt{16}*\sqrt{40030}=4\sqrt{40030}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-800)-4\sqrt{40030}}{2*-40}=\frac{800-4\sqrt{40030}}{-80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-800)+4\sqrt{40030}}{2*-40}=\frac{800+4\sqrt{40030}}{-80}
$