7=2x2+10x

Solution for 7=2x2+10x equation:

7=2x^2+10x

We move all terms to the left:

7-(2x^2+10x)=0

We get rid of parentheses

-2x^2-10x+7=0

a = -2; b = -10; c = +7;
Δ = b2-4ac
Δ = -102-4·(-2)·7
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{39}}{2*-2}=\frac{10-2\sqrt{39}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{39}}{2*-2}=\frac{10+2\sqrt{39}}{-4}
$