4x+3=5/2x-7

Solution for 4x+3=5/2x-7 equation:

4x+3=5/2x-7

We move all terms to the left:

4x+3-(5/2x-7)=0


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

x∈R


We get rid of parentheses

4x-5/2x+7+3=0

We multiply all the terms by the denominator


4x*2x+7*2x+3*2x-5=0

Wy multiply elements

8x^2+14x+6x-5=0

We add all the numbers together, and all the variables

8x^2+20x-5=0

a = 8; b = 20; c = -5;
Δ = b2-4ac
Δ = 202-4·8·(-5)
Δ = 560
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:

$\sqrt{\Delta}=\sqrt{560}=\sqrt{16*35}=\sqrt{16}*\sqrt{35}=4\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{35}}{2*8}=\frac{-20-4\sqrt{35}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{35}}{2*8}=\frac{-20+4\sqrt{35}}{16}
$