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3x^2-11x-4=04x^2+8x+3=0
We move all terms to the left:
3x^2-11x-4-(04x^2+8x+3)=0
We get rid of parentheses
3x^2-04x^2-11x-8x-3-4=0
We add all the numbers together, and all the variables
-1x^2-19x-7=0
a = -1; b = -19; c = -7;
Δ = b2-4ac
Δ = -192-4·(-1)·(-7)
Δ = 333
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{333}=\sqrt{9*37}=\sqrt{9}*\sqrt{37}=3\sqrt{37}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-3\sqrt{37}}{2*-1}=\frac{19-3\sqrt{37}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+3\sqrt{37}}{2*-1}=\frac{19+3\sqrt{37}}{-2} $
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