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x+2=22-7/8x-15
We move all terms to the left:
x+2-(22-7/8x-15)=0
Domain of the equation: 8x-15)!=0We add all the numbers together, and all the variables
x∈R
x-(-7/8x+7)+2=0
We get rid of parentheses
x+7/8x-7+2=0
We multiply all the terms by the denominator
x*8x-7*8x+2*8x+7=0
Wy multiply elements
8x^2-56x+16x+7=0
We add all the numbers together, and all the variables
8x^2-40x+7=0
a = 8; b = -40; c = +7;
Δ = b2-4ac
Δ = -402-4·8·7
Δ = 1376
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1376}=\sqrt{16*86}=\sqrt{16}*\sqrt{86}=4\sqrt{86}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{86}}{2*8}=\frac{40-4\sqrt{86}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{86}}{2*8}=\frac{40+4\sqrt{86}}{16} $
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