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9x+10-7x=5(x-2)8x-5=5(x-4)
We move all terms to the left:
9x+10-7x-(5(x-2)8x-5)=0
We add all the numbers together, and all the variables
2x-(5(x-2)8x-5)+10=0
We calculate terms in parentheses: -(5(x-2)8x-5), so:We get rid of parentheses
5(x-2)8x-5
We multiply parentheses
40x^2-80x-5
Back to the equation:
-(40x^2-80x-5)
-40x^2+2x+80x+5+10=0
We add all the numbers together, and all the variables
-40x^2+82x+15=0
a = -40; b = 82; c = +15;
Δ = b2-4ac
Δ = 822-4·(-40)·15
Δ = 9124
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9124}=\sqrt{4*2281}=\sqrt{4}*\sqrt{2281}=2\sqrt{2281}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(82)-2\sqrt{2281}}{2*-40}=\frac{-82-2\sqrt{2281}}{-80} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(82)+2\sqrt{2281}}{2*-40}=\frac{-82+2\sqrt{2281}}{-80} $
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