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10-4x=6x^2+14x
We move all terms to the left:
10-4x-(6x^2+14x)=0
We get rid of parentheses
-6x^2-4x-14x+10=0
We add all the numbers together, and all the variables
-6x^2-18x+10=0
a = -6; b = -18; c = +10;
Δ = b2-4ac
Δ = -182-4·(-6)·10
Δ = 564
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{564}=\sqrt{4*141}=\sqrt{4}*\sqrt{141}=2\sqrt{141}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{141}}{2*-6}=\frac{18-2\sqrt{141}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{141}}{2*-6}=\frac{18+2\sqrt{141}}{-12} $
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