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3x^2+5x-2=7x+15
We move all terms to the left:
3x^2+5x-2-(7x+15)=0
We get rid of parentheses
3x^2+5x-7x-15-2=0
We add all the numbers together, and all the variables
3x^2-2x-17=0
a = 3; b = -2; c = -17;
Δ = b2-4ac
Δ = -22-4·3·(-17)
Δ = 208
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{13}}{2*3}=\frac{2-4\sqrt{13}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{13}}{2*3}=\frac{2+4\sqrt{13}}{6} $
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