1/2x+7(4x-9)=22.5

Solution for 1/2x+7(4x-9)=22.5 equation:

1/2x+7(4x-9)=22.5

We move all terms to the left:

1/2x+7(4x-9)-(22.5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x+7(4x-9)-22.5=0

We multiply parentheses

1/2x+28x-63-22.5=0

We multiply all the terms by the denominator


28x*2x-63*2x-(22.5)*2x+1=0

We multiply parentheses

28x*2x-63*2x-45x+1=0

Wy multiply elements

56x^2-126x-45x+1=0

We add all the numbers together, and all the variables

56x^2-171x+1=0

a = 56; b = -171; c = +1;
Δ = b2-4ac
Δ = -1712-4·56·1
Δ = 29017
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-171)-\sqrt{29017}}{2*56}=\frac{171-\sqrt{29017}}{112}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-171)+\sqrt{29017}}{2*56}=\frac{171+\sqrt{29017}}{112}
$