4x=5/2x-7

Solution for 4x=5/2x-7 equation:

4x=5/2x-7

We move all terms to the left:

4x-(5/2x-7)=0


Domain of the equation: 2x-7)!=0

x∈R


We get rid of parentheses

4x-5/2x+7=0

We multiply all the terms by the denominator


4x*2x+7*2x-5=0

Wy multiply elements

8x^2+14x-5=0

a = 8; b = 14; c = -5;
Δ = b2-4ac
Δ = 142-4·8·(-5)
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{89}}{2*8}=\frac{-14-2\sqrt{89}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{89}}{2*8}=\frac{-14+2\sqrt{89}}{16}
$