3x+9=1/2*7x+10

Solution for 3x+9=1/2*7x+10 equation:

3x+9=1/2*7x+10

We move all terms to the left:

3x+9-(1/2*7x+10)=0


Domain of the equation: 2*7x+10)!=0

x∈R


We get rid of parentheses

3x-1/2*7x-10+9=0

We multiply all the terms by the denominator


3x*2*7x-10*2*7x+9*2*7x-1=0

Wy multiply elements

42x^2*7-140x*7+126x*7-1=0

Wy multiply elements

294x^2-980x+882x-1=0

We add all the numbers together, and all the variables

294x^2-98x-1=0

a = 294; b = -98; c = -1;
Δ = b2-4ac
Δ = -982-4·294·(-1)
Δ = 10780
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:

$\sqrt{\Delta}=\sqrt{10780}=\sqrt{196*55}=\sqrt{196}*\sqrt{55}=14\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-98)-14\sqrt{55}}{2*294}=\frac{98-14\sqrt{55}}{588}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-98)+14\sqrt{55}}{2*294}=\frac{98+14\sqrt{55}}{588}
$