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-5(x2-5)-3x-5=7
We move all terms to the left:
-5(x2-5)-3x-5-(7)=0
We add all the numbers together, and all the variables
-5(+x^2-5)-3x-5-7=0
We add all the numbers together, and all the variables
-5(+x^2-5)-3x-12=0
We multiply parentheses
-5x^2-3x+25-12=0
We add all the numbers together, and all the variables
-5x^2-3x+13=0
a = -5; b = -3; c = +13;
Δ = b2-4ac
Δ = -32-4·(-5)·13
Δ = 269
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{269}}{2*-5}=\frac{3-\sqrt{269}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{269}}{2*-5}=\frac{3+\sqrt{269}}{-10} $
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