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2/5x+4=6x+5-7
We move all terms to the left:
2/5x+4-(6x+5-7)=0
Domain of the equation: 5x!=0We add all the numbers together, and all the variables
x!=0/5
x!=0
x∈R
2/5x-(6x-2)+4=0
We get rid of parentheses
2/5x-6x+2+4=0
We multiply all the terms by the denominator
-6x*5x+2*5x+4*5x+2=0
Wy multiply elements
-30x^2+10x+20x+2=0
We add all the numbers together, and all the variables
-30x^2+30x+2=0
a = -30; b = 30; c = +2;
Δ = b2-4ac
Δ = 302-4·(-30)·2
Δ = 1140
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1140}=\sqrt{4*285}=\sqrt{4}*\sqrt{285}=2\sqrt{285}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{285}}{2*-30}=\frac{-30-2\sqrt{285}}{-60} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{285}}{2*-30}=\frac{-30+2\sqrt{285}}{-60} $
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