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6x^2+6x-4=85/2
We move all terms to the left:
6x^2+6x-4-(85/2)=0
We add all the numbers together, and all the variables
6x^2+6x-4-(+85/2)=0
We get rid of parentheses
6x^2+6x-4-85/2=0
We multiply all the terms by the denominator
6x^2*2+6x*2-85-4*2=0
We add all the numbers together, and all the variables
6x^2*2+6x*2-93=0
Wy multiply elements
12x^2+12x-93=0
a = 12; b = 12; c = -93;
Δ = b2-4ac
Δ = 122-4·12·(-93)
Δ = 4608
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4608}=\sqrt{2304*2}=\sqrt{2304}*\sqrt{2}=48\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-48\sqrt{2}}{2*12}=\frac{-12-48\sqrt{2}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+48\sqrt{2}}{2*12}=\frac{-12+48\sqrt{2}}{24} $
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