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X^2+31X+70=17X+40
We move all terms to the left:
X^2+31X+70-(17X+40)=0
We get rid of parentheses
X^2+31X-17X-40+70=0
We add all the numbers together, and all the variables
X^2+14X+30=0
a = 1; b = 14; c = +30;
Δ = b2-4ac
Δ = 142-4·1·30
Δ = 76
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{19}}{2*1}=\frac{-14-2\sqrt{19}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{19}}{2*1}=\frac{-14+2\sqrt{19}}{2} $
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