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(2/3)(5x+7)=8x
We move all terms to the left:
(2/3)(5x+7)-(8x)=0
Domain of the equation: 3)(5x+7)!=0We add all the numbers together, and all the variables
x∈R
(+2/3)(5x+7)-8x=0
We add all the numbers together, and all the variables
-8x+(+2/3)(5x+7)=0
We multiply parentheses ..
(+10x^2+2/3*7)-8x=0
We multiply all the terms by the denominator
(+10x^2+2-8x*3*7)=0
We get rid of parentheses
10x^2-8x*3*7+2=0
Wy multiply elements
10x^2-168x*7+2=0
Wy multiply elements
10x^2-1176x+2=0
a = 10; b = -1176; c = +2;
Δ = b2-4ac
Δ = -11762-4·10·2
Δ = 1382896
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1382896}=\sqrt{16*86431}=\sqrt{16}*\sqrt{86431}=4\sqrt{86431}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1176)-4\sqrt{86431}}{2*10}=\frac{1176-4\sqrt{86431}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1176)+4\sqrt{86431}}{2*10}=\frac{1176+4\sqrt{86431}}{20} $
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