3/2x-7=-7x+22

Solution for 3/2x-7=-7x+22 equation:

3/2x-7=-7x+22

We move all terms to the left:

3/2x-7-(-7x+22)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

3/2x+7x-22-7=0

We multiply all the terms by the denominator


7x*2x-22*2x-7*2x+3=0

Wy multiply elements

14x^2-44x-14x+3=0

We add all the numbers together, and all the variables

14x^2-58x+3=0

a = 14; b = -58; c = +3;
Δ = b2-4ac
Δ = -582-4·14·3
Δ = 3196
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:

$\sqrt{\Delta}=\sqrt{3196}=\sqrt{4*799}=\sqrt{4}*\sqrt{799}=2\sqrt{799}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-58)-2\sqrt{799}}{2*14}=\frac{58-2\sqrt{799}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-58)+2\sqrt{799}}{2*14}=\frac{58+2\sqrt{799}}{28}
$