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5x+3x^2-8x^2+2x-9+12=0
We add all the numbers together, and all the variables
-5x^2+7x+3=0
a = -5; b = 7; c = +3;
Δ = b2-4ac
Δ = 72-4·(-5)·3
Δ = 109
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{-(7)-\sqrt{109}}{2*-5}=\frac{-7-\sqrt{109}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{109}}{2*-5}=\frac{-7+\sqrt{109}}{-10} $
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