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3x(0.5x+1)-7=8
We move all terms to the left:
3x(0.5x+1)-7-(8)=0
We add all the numbers together, and all the variables
3x(0.5x+1)-15=0
We multiply parentheses
0x^2+3x-15=0
We add all the numbers together, and all the variables
x^2+3x-15=0
a = 1; b = 3; c = -15;
Δ = b2-4ac
Δ = 32-4·1·(-15)
Δ = 69
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{-(3)-\sqrt{69}}{2*1}=\frac{-3-\sqrt{69}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{69}}{2*1}=\frac{-3+\sqrt{69}}{2} $
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