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11-7x^2=-157
We move all terms to the left:
11-7x^2-(-157)=0
We add all the numbers together, and all the variables
-7x^2+168=0
a = -7; b = 0; c = +168;
Δ = b2-4ac
Δ = 02-4·(-7)·168
Δ = 4704
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4704}=\sqrt{784*6}=\sqrt{784}*\sqrt{6}=28\sqrt{6}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28\sqrt{6}}{2*-7}=\frac{0-28\sqrt{6}}{-14} =-\frac{28\sqrt{6}}{-14} =-\frac{2\sqrt{6}}{-1} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28\sqrt{6}}{2*-7}=\frac{0+28\sqrt{6}}{-14} =\frac{28\sqrt{6}}{-14} =\frac{2\sqrt{6}}{-1} $
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