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-2x+3x=5x^2+12x-3
We move all terms to the left:
-2x+3x-(5x^2+12x-3)=0
We add all the numbers together, and all the variables
x-(5x^2+12x-3)=0
We get rid of parentheses
-5x^2+x-12x+3=0
We add all the numbers together, and all the variables
-5x^2-11x+3=0
a = -5; b = -11; c = +3;
Δ = b2-4ac
Δ = -112-4·(-5)·3
Δ = 181
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{-(-11)-\sqrt{181}}{2*-5}=\frac{11-\sqrt{181}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{181}}{2*-5}=\frac{11+\sqrt{181}}{-10} $
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