5x-45=-3/2x+7

Solution for 5x-45=-3/2x+7 equation:

5x-45=-3/2x+7

We move all terms to the left:

5x-45-(-3/2x+7)=0


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

x∈R


We get rid of parentheses

5x+3/2x-7-45=0

We multiply all the terms by the denominator


5x*2x-7*2x-45*2x+3=0

Wy multiply elements

10x^2-14x-90x+3=0

We add all the numbers together, and all the variables

10x^2-104x+3=0

a = 10; b = -104; c = +3;
Δ = b2-4ac
Δ = -1042-4·10·3
Δ = 10696
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:

$\sqrt{\Delta}=\sqrt{10696}=\sqrt{4*2674}=\sqrt{4}*\sqrt{2674}=2\sqrt{2674}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-104)-2\sqrt{2674}}{2*10}=\frac{104-2\sqrt{2674}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-104)+2\sqrt{2674}}{2*10}=\frac{104+2\sqrt{2674}}{20}
$