5x-7=3/2x+15

Solution for 5x-7=3/2x+15 equation:

5x-7=3/2x+15

We move all terms to the left:

5x-7-(3/2x+15)=0


Domain of the equation: 2x+15)!=0

x∈R


We get rid of parentheses

5x-3/2x-15-7=0

We multiply all the terms by the denominator


5x*2x-15*2x-7*2x-3=0

Wy multiply elements

10x^2-30x-14x-3=0

We add all the numbers together, and all the variables

10x^2-44x-3=0

a = 10; b = -44; c = -3;
Δ = b2-4ac
Δ = -442-4·10·(-3)
Δ = 2056
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:

$\sqrt{\Delta}=\sqrt{2056}=\sqrt{4*514}=\sqrt{4}*\sqrt{514}=2\sqrt{514}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-2\sqrt{514}}{2*10}=\frac{44-2\sqrt{514}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+2\sqrt{514}}{2*10}=\frac{44+2\sqrt{514}}{20}
$