x=-3/2x+7

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

x=-3/2x+7

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

x+3/2x-7=0

We multiply all the terms by the denominator


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

Wy multiply elements

2x^2-14x+3=0

a = 2; b = -14; c = +3;
Δ = b2-4ac
Δ = -142-4·2·3
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{43}}{2*2}=\frac{14-2\sqrt{43}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{43}}{2*2}=\frac{14+2\sqrt{43}}{4}
$