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2x^2+5x-3=5x^2+17x-12
We move all terms to the left:
2x^2+5x-3-(5x^2+17x-12)=0
We get rid of parentheses
2x^2-5x^2+5x-17x+12-3=0
We add all the numbers together, and all the variables
-3x^2-12x+9=0
a = -3; b = -12; c = +9;
Δ = b2-4ac
Δ = -122-4·(-3)·9
Δ = 252
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{7}}{2*-3}=\frac{12-6\sqrt{7}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{7}}{2*-3}=\frac{12+6\sqrt{7}}{-6} $
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