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0.25x+7=(1)/(3)x-8
We move all terms to the left:
0.25x+7-((1)/(3)x-8)=0
Domain of the equation: 3x-8)!=0We get rid of parentheses
x∈R
0.25x-1/3x+8+7=0
We multiply all the terms by the denominator
(0.25x)*3x+8*3x+7*3x-1=0
We add all the numbers together, and all the variables
(+0.25x)*3x+8*3x+7*3x-1=0
We multiply parentheses
0x^2+8*3x+7*3x-1=0
Wy multiply elements
0x^2+24x+21x-1=0
We add all the numbers together, and all the variables
x^2+45x-1=0
a = 1; b = 45; c = -1;
Δ = b2-4ac
Δ = 452-4·1·(-1)
Δ = 2029
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{-(45)-\sqrt{2029}}{2*1}=\frac{-45-\sqrt{2029}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{2029}}{2*1}=\frac{-45+\sqrt{2029}}{2} $
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