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4x^2=23x+6
We move all terms to the left:
4x^2-(23x+6)=0
We get rid of parentheses
4x^2-23x-6=0
a = 4; b = -23; c = -6;
Δ = b2-4ac
Δ = -232-4·4·(-6)
Δ = 625
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{625}=25$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-25}{2*4}=\frac{-2}{8} =-1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+25}{2*4}=\frac{48}{8} =6 $
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