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8x^2+9x-6=3x+7
We move all terms to the left:
8x^2+9x-6-(3x+7)=0
We get rid of parentheses
8x^2+9x-3x-7-6=0
We add all the numbers together, and all the variables
8x^2+6x-13=0
a = 8; b = 6; c = -13;
Δ = b2-4ac
Δ = 62-4·8·(-13)
Δ = 452
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{452}=\sqrt{4*113}=\sqrt{4}*\sqrt{113}=2\sqrt{113}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{113}}{2*8}=\frac{-6-2\sqrt{113}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{113}}{2*8}=\frac{-6+2\sqrt{113}}{16} $
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