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2/3x+4x=70
We move all terms to the left:
2/3x+4x-(70)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
4x+2/3x-70=0
We multiply all the terms by the denominator
4x*3x-70*3x+2=0
Wy multiply elements
12x^2-210x+2=0
a = 12; b = -210; c = +2;
Δ = b2-4ac
Δ = -2102-4·12·2
Δ = 44004
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{44004}=\sqrt{4*11001}=\sqrt{4}*\sqrt{11001}=2\sqrt{11001}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-210)-2\sqrt{11001}}{2*12}=\frac{210-2\sqrt{11001}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-210)+2\sqrt{11001}}{2*12}=\frac{210+2\sqrt{11001}}{24} $
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