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-3/4x+7=3^x+2
We move all terms to the left:
-3/4x+7-(3^x+2)=0
Domain of the equation: 4x!=0We get rid of parentheses
x!=0/4
x!=0
x∈R
-3/4x-3^x-2+7=0
We multiply all the terms by the denominator
-3^x*4x-2*4x+7*4x-3=0
Wy multiply elements
-12x^2-8x+28x-3=0
We add all the numbers together, and all the variables
-12x^2+20x-3=0
a = -12; b = 20; c = -3;
Δ = b2-4ac
Δ = 202-4·(-12)·(-3)
Δ = 256
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{256}=16$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-16}{2*-12}=\frac{-36}{-24} =1+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+16}{2*-12}=\frac{-4}{-24} =1/6 $
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