10x-15/2x-3=0

Solution for 10x-15/2x-3=0 equation:

10x-15/2x-3=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


10x*2x-3*2x-15=0

Wy multiply elements

20x^2-6x-15=0

a = 20; b = -6; c = -15;
Δ = b2-4ac
Δ = -62-4·20·(-15)
Δ = 1236
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:

$\sqrt{\Delta}=\sqrt{1236}=\sqrt{4*309}=\sqrt{4}*\sqrt{309}=2\sqrt{309}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{309}}{2*20}=\frac{6-2\sqrt{309}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{309}}{2*20}=\frac{6+2\sqrt{309}}{40}
$