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X^2+3X-7/4=0
We multiply all the terms by the denominator
X^2*4+3X*4-7=0
Wy multiply elements
4X^2+12X-7=0
a = 4; b = 12; c = -7;
Δ = b2-4ac
Δ = 122-4·4·(-7)
Δ = 256
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{256}=16$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-16}{2*4}=\frac{-28}{8} =-3+1/2 $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+16}{2*4}=\frac{4}{8} =1/2 $
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