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(2/5x+90)+(3x-2)=180
We move all terms to the left:
(2/5x+90)+(3x-2)-(180)=0
Domain of the equation: 5x+90)!=0We get rid of parentheses
x∈R
2/5x+3x+90-2-180=0
We multiply all the terms by the denominator
3x*5x+90*5x-2*5x-180*5x+2=0
Wy multiply elements
15x^2+450x-10x-900x+2=0
We add all the numbers together, and all the variables
15x^2-460x+2=0
a = 15; b = -460; c = +2;
Δ = b2-4ac
Δ = -4602-4·15·2
Δ = 211480
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{211480}=\sqrt{4*52870}=\sqrt{4}*\sqrt{52870}=2\sqrt{52870}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-460)-2\sqrt{52870}}{2*15}=\frac{460-2\sqrt{52870}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-460)+2\sqrt{52870}}{2*15}=\frac{460+2\sqrt{52870}}{30} $
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