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(1/10)(x+50)=-3x-13+4x
We move all terms to the left:
(1/10)(x+50)-(-3x-13+4x)=0
Domain of the equation: 10)(x+50)!=0We add all the numbers together, and all the variables
x∈R
(+1/10)(x+50)-(x-13)=0
We get rid of parentheses
(+1/10)(x+50)-x+13=0
We multiply parentheses ..
(+x^2+1/10*50)-x+13=0
We multiply all the terms by the denominator
(+x^2+1-x*10*50)+13*10*50)=0
We add all the numbers together, and all the variables
(+x^2+1-x*10*50)=0
We get rid of parentheses
x^2-x*10*50+1=0
Wy multiply elements
x^2-500x*5+1=0
Wy multiply elements
x^2-2500x+1=0
a = 1; b = -2500; c = +1;
Δ = b2-4ac
Δ = -25002-4·1·1
Δ = 6249996
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6249996}=\sqrt{36*173611}=\sqrt{36}*\sqrt{173611}=6\sqrt{173611}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2500)-6\sqrt{173611}}{2*1}=\frac{2500-6\sqrt{173611}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2500)+6\sqrt{173611}}{2*1}=\frac{2500+6\sqrt{173611}}{2} $
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