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0=4x^2+6x-3
We move all terms to the left:
0-(4x^2+6x-3)=0
We add all the numbers together, and all the variables
-(4x^2+6x-3)=0
We get rid of parentheses
-4x^2-6x+3=0
a = -4; b = -6; c = +3;
Δ = b2-4ac
Δ = -62-4·(-4)·3
Δ = 84
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{21}}{2*-4}=\frac{6-2\sqrt{21}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{21}}{2*-4}=\frac{6+2\sqrt{21}}{-8} $
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