5x^2=7x+49

Solution for 5x^2=7x+49 equation:

5x^2=7x+49

We move all terms to the left:

5x^2-(7x+49)=0

We get rid of parentheses

5x^2-7x-49=0

a = 5; b = -7; c = -49;
Δ = b2-4ac
Δ = -72-4·5·(-49)
Δ = 1029
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:

$\sqrt{\Delta}=\sqrt{1029}=\sqrt{49*21}=\sqrt{49}*\sqrt{21}=7\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7\sqrt{21}}{2*5}=\frac{7-7\sqrt{21}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7\sqrt{21}}{2*5}=\frac{7+7\sqrt{21}}{10}
$