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(-5x^2+2x-6)+(-5x^2+2x-6)=6x-14
We move all terms to the left:
(-5x^2+2x-6)+(-5x^2+2x-6)-(6x-14)=0
We get rid of parentheses
-5x^2-5x^2+2x+2x-6x-6-6+14=0
We add all the numbers together, and all the variables
-10x^2-2x+2=0
a = -10; b = -2; c = +2;
Δ = b2-4ac
Δ = -22-4·(-10)·2
Δ = 84
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{21}}{2*-10}=\frac{2-2\sqrt{21}}{-20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{21}}{2*-10}=\frac{2+2\sqrt{21}}{-20} $
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