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-2x^2+3x=4x-15
We move all terms to the left:
-2x^2+3x-(4x-15)=0
We get rid of parentheses
-2x^2+3x-4x+15=0
We add all the numbers together, and all the variables
-2x^2-1x+15=0
a = -2; b = -1; c = +15;
Δ = b2-4ac
Δ = -12-4·(-2)·15
Δ = 121
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{121}=11$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-11}{2*-2}=\frac{-10}{-4} =2+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+11}{2*-2}=\frac{12}{-4} =-3 $
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