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6a^2+8a-25=-3
We move all terms to the left:
6a^2+8a-25-(-3)=0
We add all the numbers together, and all the variables
6a^2+8a-22=0
a = 6; b = 8; c = -22;
Δ = b2-4ac
Δ = 82-4·6·(-22)
Δ = 592
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{37}}{2*6}=\frac{-8-4\sqrt{37}}{12} $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{37}}{2*6}=\frac{-8+4\sqrt{37}}{12} $
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