7a^2-15=-10a

Solution for 7a^2-15=-10a equation:

7a^2-15=-10a

We move all terms to the left:

7a^2-15-(-10a)=0

We get rid of parentheses

7a^2+10a-15=0

a = 7; b = 10; c = -15;
Δ = b2-4ac
Δ = 102-4·7·(-15)
Δ = 520
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{520}=\sqrt{4*130}=\sqrt{4}*\sqrt{130}=2\sqrt{130}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{130}}{2*7}=\frac{-10-2\sqrt{130}}{14}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{130}}{2*7}=\frac{-10+2\sqrt{130}}{14}
$