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18-x+5=10x^2+-10
We move all terms to the left:
18-x+5-(10x^2+-10)=0
We add all the numbers together, and all the variables
-1x-(10x^2+-10)+23=0
We use the square of the difference formula
-1x-(10x^2-10)+23=0
We get rid of parentheses
-10x^2-1x+10+23=0
We add all the numbers together, and all the variables
-10x^2-1x+33=0
a = -10; b = -1; c = +33;
Δ = b2-4ac
Δ = -12-4·(-10)·33
Δ = 1321
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{-(-1)-\sqrt{1321}}{2*-10}=\frac{1-\sqrt{1321}}{-20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{1321}}{2*-10}=\frac{1+\sqrt{1321}}{-20} $
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