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x^2+49=15x+15
We move all terms to the left:
x^2+49-(15x+15)=0
We get rid of parentheses
x^2-15x-15+49=0
We add all the numbers together, and all the variables
x^2-15x+34=0
a = 1; b = -15; c = +34;
Δ = b2-4ac
Δ = -152-4·1·34
Δ = 89
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{-(-15)-\sqrt{89}}{2*1}=\frac{15-\sqrt{89}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{89}}{2*1}=\frac{15+\sqrt{89}}{2} $
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