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(3/7)(x+3)+5=3x+2
We move all terms to the left:
(3/7)(x+3)+5-(3x+2)=0
Domain of the equation: 7)(x+3)!=0We add all the numbers together, and all the variables
x∈R
(+3/7)(x+3)-(3x+2)+5=0
We get rid of parentheses
(+3/7)(x+3)-3x-2+5=0
We multiply parentheses ..
(+3x^2+3/7*3)-3x-2+5=0
We multiply all the terms by the denominator
(+3x^2+3-3x*7*3)-2*7*3)+5*7*3)=0
We add all the numbers together, and all the variables
(+3x^2+3-3x*7*3)=0
We get rid of parentheses
3x^2-3x*7*3+3=0
Wy multiply elements
3x^2-63x*3+3=0
Wy multiply elements
3x^2-189x+3=0
a = 3; b = -189; c = +3;
Δ = b2-4ac
Δ = -1892-4·3·3
Δ = 35685
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{35685}=\sqrt{9*3965}=\sqrt{9}*\sqrt{3965}=3\sqrt{3965}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-189)-3\sqrt{3965}}{2*3}=\frac{189-3\sqrt{3965}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-189)+3\sqrt{3965}}{2*3}=\frac{189+3\sqrt{3965}}{6} $
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