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2x^2-11=-4x^2+15x-3
We move all terms to the left:
2x^2-11-(-4x^2+15x-3)=0
We get rid of parentheses
2x^2+4x^2-15x+3-11=0
We add all the numbers together, and all the variables
6x^2-15x-8=0
a = 6; b = -15; c = -8;
Δ = b2-4ac
Δ = -152-4·6·(-8)
Δ = 417
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{417}}{2*6}=\frac{15-\sqrt{417}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{417}}{2*6}=\frac{15+\sqrt{417}}{12} $
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