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3x^2+5x-37=-x^2-7x+55
We move all terms to the left:
3x^2+5x-37-(-x^2-7x+55)=0
We get rid of parentheses
3x^2+x^2+7x+5x-55-37=0
We add all the numbers together, and all the variables
4x^2+12x-92=0
a = 4; b = 12; c = -92;
Δ = b2-4ac
Δ = 122-4·4·(-92)
Δ = 1616
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1616}=\sqrt{16*101}=\sqrt{16}*\sqrt{101}=4\sqrt{101}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{101}}{2*4}=\frac{-12-4\sqrt{101}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{101}}{2*4}=\frac{-12+4\sqrt{101}}{8} $
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