10-7x2=-3x+5

Solution for 10-7x2=-3x+5 equation:

10-7x^2=-3x+5

We move all terms to the left:

10-7x^2-(-3x+5)=0

We get rid of parentheses

-7x^2+3x-5+10=0

We add all the numbers together, and all the variables

-7x^2+3x+5=0

a = -7; b = 3; c = +5;
Δ = b2-4ac
Δ = 32-4·(-7)·5
Δ = 149
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{-(3)-\sqrt{149}}{2*-7}=\frac{-3-\sqrt{149}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{149}}{2*-7}=\frac{-3+\sqrt{149}}{-14}
$