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7x^2+3-x-40=2x^2-15x+70
We move all terms to the left:
7x^2+3-x-40-(2x^2-15x+70)=0
We add all the numbers together, and all the variables
7x^2-1x-(2x^2-15x+70)-37=0
We get rid of parentheses
7x^2-2x^2-1x+15x-70-37=0
We add all the numbers together, and all the variables
5x^2+14x-107=0
a = 5; b = 14; c = -107;
Δ = b2-4ac
Δ = 142-4·5·(-107)
Δ = 2336
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2336}=\sqrt{16*146}=\sqrt{16}*\sqrt{146}=4\sqrt{146}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-4\sqrt{146}}{2*5}=\frac{-14-4\sqrt{146}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+4\sqrt{146}}{2*5}=\frac{-14+4\sqrt{146}}{10} $
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