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6x^2-8x+4=-2x^2-6x+15
We move all terms to the left:
6x^2-8x+4-(-2x^2-6x+15)=0
We get rid of parentheses
6x^2+2x^2+6x-8x-15+4=0
We add all the numbers together, and all the variables
8x^2-2x-11=0
a = 8; b = -2; c = -11;
Δ = b2-4ac
Δ = -22-4·8·(-11)
Δ = 356
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{89}}{2*8}=\frac{2-2\sqrt{89}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{89}}{2*8}=\frac{2+2\sqrt{89}}{16} $
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